Content

• To step
• Part 1 of 5: Learning the basic rules of algebra
• Part 2 of 5: Understanding variables
• Part 3 of 5: Solving equations by eliminating
• Part 4 of 5: Hone your math skills
• Part 5 of 5: Exploring advanced topics
• Tips

Learning algebra is important to be able to progress with almost any part of math in secondary and higher education. Every level of math is built on the foundation, and with that, every math level is particularly important. However, even the most basic math skills can be difficult for beginners to grasp when confronted with them for the first time. If you are struggling with basic algebra topics, don't worry. With a little explanation, a few simple examples and some tips to improve your skills, you'll soon be a master at algebra.

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Part 1 of 5: Learning the basic rules of algebra

1. Review basic math skills. To learn algebra you will need to know the basic skills such as addition, subtraction, multiplication and division. These math skills as you learn them in primary school are essential before you start algebra. If you have not mastered these skills, it will be difficult to learn the more complex concepts covered in algebra. If you need a refresher on these operations, check out wikiHow for articles on the basics of arithmetic.
   • It is not necessary to be very good at mental arithmetic to be able to do algebra well. Often you will be allowed to work with a calculator during math class to save time while doing the simple sums. In any case, you should be able to do math without a calculator, in case you are not allowed to use it.
2. Learn the order of operations. One of the trickiest things when it comes to solving a math equation is knowing where to start. Fortunately, there is a particular order in which these tasks solves: first come, the terms in parentheses, followed by the exponents / powers, then the multiplication, division, addition, and subtraction in the end. A useful mnemonic to remember the order of operations, "How Are We Getting rid of the failures (or acronym HMWVDOA). See wikiHow for articles on applying the order of operations. As a reminder, here is again the sequence of operations:
   • H.barrels
   • M.raise eight
   • W.root pulling
   • V.multiply
   • D.elen
   • Ocounting
   • apulling
   • The order of operations is important in math, because a wrong order can cause a different answer to be found. For example, if you have the problem 8 + 2 × 5, and you first add 2 to 8, you get 10 × 5 =50 in response. But if you multiply 2 by 5 first, then it follows that 8 + 10 =18. Only the second answer is correct.
3. Learn how to use negative numbers. In algebra, it is common to use negative numbers, so it is wise to further by observing how you add negative numbers, subtracts, multiplies and divides before you move on to algebra. Below are just some of the principles of working with negative numbers that you have to remember - for more information, see the articles on wikiHow about addition and subtraction and division and multiplication of negative numbers.
   • On a number line, a negative version of a number is as far from zero as it is on the positive side, but in the opposite direction.
   • Adding two negative numbers makes the sum more negative (in other words, the numbers are getting bigger, but because the number is negative it is a lower number).
   • Two negative signs cancel each other out - subtracting a negative number is the same as adding a positive number.
   • Multiplying or dividing two negative numbers gives a positive answer.
   • Multiplying or dividing a positive number and a negative number produces a negative answer.
4. Learn how to organize long problems. While simple algebra problems are often easy to solve, more complicated problems can take many steps to complete. To avoid mistakes, at least start on a new line every time as soon as you are one step further in solving the problem. If you are dealing with a comparison with terms on two sides of the equal sign, try to write these characters ("=") one below the other. That way, any error in your calculation will be much easier to spot.
   • For example, to solve the equation 9/3 - 5 + 3 × 4, we order our problem like this:

     9/3 - 5 + 3 × 4

     9/3 - 5 + 12

     3 - 5 + 12

     3 + 7

     10

Part 2 of 5: Understanding variables

1. Look for symbols that are not numbers. In algebra, you deal with letters and symbols in your math problems, instead of just numbers. These are called variables. Variables are not as difficult as they may seem - they are simply ways of representing numbers with unknown values. Below are some common examples of variables in algebra:
   • Letters such as x, y, z, a, b, and c
   • Greek letters such as theta, or θ
   • Don't notice that all symbols are unknown variables. For example, pi or π, always equals (rounded) 3.1459.
2. Think of variables as "unknown" numbers. As indicated above, variables are generally just numbers with unknown values. In other words, there is a number which can take the place of the variable to make the equation work. Usually, the purpose of an algebra problem is to figure out what that variable is - think of it as a "mysterious number" that you are trying to discover.
   • For example, in the equation 2x + 3 = 11, x is the variable. This implies that there is a certain value which can be taken to be in the place of X, to thereby the left-hand side of the equation equal to 11. As to 2 × 4 + 3 = 11, it holds in this case, x =4.
   • An easy way to understand variables is to replace them with a question mark in algebra problems. For example, rewrite the equation 2 + 3 + x = 9 as 2 + 3 + ?= 9. This is a simple way to see what the intention is - we need to figure out which number to add to 2 + 3 = 5 to get 9 as the answer. The answer is again 4, of course.
3. If a variable appears multiple times, simplify the variables. What do you do if the same variable appears several times in an equation? Although this appears to be a difficult situation, you can treat variables in the same way as a normal numbers - in other words, they can add, subtract, etc. as long as you combine only variables are the same.. In other words, x + x = 2x, but x + y is not equal to 2xy.
   • For example, look at the equation 2x + 1x = 9. In this case, we add 2x and 1x together, so that we get 3x = 9. Since 3 x 3 = 9, we now know that x =3.
   • Note again that you can only add variables that are equal to each other. In the equation 2x + 1y = 9, we cannot combine 2x and 1y, because these are two different variables.
   • This is also true when one variable has a different exponent from the other. For example: in the equation 2x + 3x = 10, 2x and 3x cannot be combined, because the x variables have different exponents. For more information on adding exponents, see wikiHow.

Part 3 of 5: Solving equations by eliminating

1. Isolate the variable in the equation. Solving an equation in algebra generally involves trying to determine what the variable is. Algebraic equations usually know numbers and / or variables on either side, like this: x + 2 = 9 × 4. To determine the variable, you will have to put to one side of the equal sign. What's left on the other side of the equal sign is the answer.
   • In the example (x + 2 = 9 × 4), to isolate x to the left of the equation, we have to get rid of the "+ 2". To do this, we subtract 2 from this side, leaving us with x = 9 × 4. To make both sides of the equation equal, we also have to subtract 2 from the other side. This leaves us with x = 9 × 4 - 2. According to the order of operations, we multiply first, then subtract, and we get the answer x = 36 - 2 =34.
2. Erase an addition by subtracting (and vice versa). As we saw above, isolating x on one side of the equal sign usually involves trying to get rid of the numbers immediately next to it. You do this by performing the "opposite" operation on both sides of the equation. For example, in the equation x + 3 = 0, we put a "- 3" on both sides, because there is a "+ 3" next to the x. This will isolate x and get "-3" on the other side of the equal sign, like this: x = -3.
   • In general, addition and subtraction are "opposite" - one works the way. See below:

     When adding, subtracting. Example: x + 9 = 3 → x = 3 - 9

     When subtracting, adding. Example: x - 4 = 20 → x = 20 + 4

3. Eliminate multiplication by dividing (and vice versa). Multiplication and division are a bit trickier to work with than addition and subtraction, but they share the same "opposite" relationship. If you see a "× 3" on one side, you can eliminate it by dividing both sides by 3.
   • With multiplication and division, you have to do the opposite operation on everything on the other side of the equal sign, even if it is more than one number. See below:

     When multiplying, dividing. Example: 6x = 14 + 2 → x = (14 + 2)/6

     When dividing, multiply. Example: x / 5 = 25 → x = 25 × 5

4. Eliminate exponents by rooting (and vice versa). Exponents is an advanced topic in algebra - if you don't know what to do with it, read the beginner's wikiHow article on exponents. The "opposite" of an exponent is the square root of that number. For example, the opposite of the exponent is the square root (√), the opposite of the exponent is the cube root (√), etc.
   • This can be a bit confusing, but in these cases you take the square root of both sides when dealing with an exponent. On the other hand, you also take the exponent of both sides when you are dealing with a square root. See below:

     For exponents, take the square root. Example: x = 49 → x =√49

     For roots, take the exponent. Example: √x = 12 → x =12

Part 4 of 5: Hone your math skills

1. Use pictures to make exercises clearer. If you are unable to present an algebra problem, use graphs or pictures to illustrate the equation. You can even use a group of objects (such as blocks or coins) if you have them handy.
   • For example, let's solve the equation x + 2 = 3 using boxes (☐)

     x + 2 = 3

     ☒+☐☐=☐☐☐

     At this point, subtract 2 from both sides by removing 2 boxes (☐☐) on both sides:

     ☒+☐☐-☐☐=☐☐☐-☐☐

     ☒ = ☐, or x =1

   • Another example: 2x = 4

     ☒☒=☐☐☐☐

     At this point, we divide both sides by two, dividing the boxes on each side into two groups:

     ☒|☒=☐☐|☐☐

     ☒ = ☐☐, or x =2

2. Use "logic controls" (especially when it comes to issues). When you need to convert a problem to an algebraic equation, check your formula by incorporating simple values ​​into the variables. Is your equation correct when x = 0? When x = 1? When x = -1? It's easy to make small mistakes while noting something like p = 6d when you mean p = d / 6, but you'll find them soon enough if you check the work you've done before moving on.
   • For example: Suppose we have a football field that is 30 meters longer than it is wide. We use the equation l = w + 30 to represent this. We can test this equation by entering simple values ​​for w. For example, if the field is w = 10 meters wide, it will be 10 + 30 = 40 meters long. If it is 30 meters wide, it will be 30 + 30 = 60 meters long, etc. This seems logical - we expect the field to get longer as it widens, so this equation seems a reasonable solution.
3. Keep in mind that answers are not always integers in math. Answers in algebra and other mathematics are not always round, easy numbers. They are often decimals, fractions or irrational numbers. A calculator can help you find these complicated answers, but keep in mind that your teacher may ask you to give the exact answer, not a clumsy decimal place.
   • For example, suppose we have reduced an algebraic equation to x = 1250. If we enter 1250 into a calculator, we get a huge string of decimal places (because the calculator's screen has limited space, it can't show the full answer). In this case, we can simply display the answer as 1250 or simplify the answer by writing it in scientific notation.
4. If you are familiar with the basics of algebra, try Factors. One of the trickier skills in algebra is factorization - sort of a shortcut for writing complex equations in a simpler form. Factoring is a fairly advanced topic in algebra, so see the article linked above if you find it a difficult topic. Below are some tips to help you factorize equations:
   • Equations of the form ax + ba factor into to a (x + b). Example: 2x + 4 = 2 (x + 2)
   • Equations of the form ax + bx factor to cx ((a / c) x + (b / c)) where c is the largest number that fully fits a and b. Example: 3y + 12y = 3y (y + 4)
   • Equations of the form x + bx + c factor to (x + y) (x + z) where y × z = c and yx + zx = bx. Example: x + 4x + 3 = (x + 3) (x + 1).
5. Practice, practice, practice! Progression in learning algebra (and any other branch of mathematics) requires a lot of hard work and repetition. Don't worry - by paying attention in class, doing all your homework, and asking for help from your teacher or other students when needed, algebra will eventually become second nature.
6. Ask your teacher to help you with the trickier topics. If you find it difficult to master the material, don't worry - you don't have to learn it on your own. Your teacher is the first person to assist you with questions. After class, politely ask the teacher for help. Good teachers are usually willing to explain a topic again when you come to them after class, and may even be able to provide you with additional practice material.
   • If for some reason your teacher can't help you, ask them about the options for tutoring at school. Many schools do have some form of extra classes that give you the extra time and attention you need to excel in algebra. Remember, taking advantage of free help available isn't something to be ashamed of - it's an indication that you're smart enough to solve your problems!

Part 5 of 5: Exploring advanced topics

1. Learn how to graph an equation. Graphs are valuable tools in algebra because they allow you to represent ideas that usually require numbers in easy-to-understand images. Usually, when starting out with algebra, graphs are limited to equations with two variables (usually x and y) and are presented in a simple 2-D graph with an x-axis and a y-axis. With these equations, all you have to do is enter a value for x, then solve for y (or vice versa) to get two numbers that correspond to a point on the graph.
   • For example, in the equation y = 3x, we enter 2 for x, and we get y = 6 as the answer. This implies the point (2,6) (two points to the right of the zero point and 6 up) is part of the graph of the equation.
   • Equations of the form y = mx + b (where m and b are numbers) are special just within the basics of algebra. These equations always have a slope m and cross the y axis at the point y = b.
2. Learn to solve inequalities. What do you do when an equation has no equal sign? Nothing special compared to what you would do otherwise, it turns out. For inequalities, where you encounter signs such as,> ("greater than") and ("less than"), solve the equation in the same way as otherwise. The answer you get is either smaller or larger than your variable.
   • For example, in the equation 3> 5x - 2, we solve it in the same way as a normal equation:

     3> 5x - 2

     5> 5x

     1> x, or x 1.

   • This implies that any number less than 1 is correct for x. In other words, x can be 0, -1, -2, etc. If we enter these numbers into the equation for x, we always get an answer less than 3.
3. Solve quadratic or square equations. An algebraic topic that many beginners stumble upon is solving quadratic equations. These are equations of the form ax + bx + c = 0, where a, b and c are numbers (except that a cannot be 0). We solve these equations with the formula x = [- b +/- √ (b - 4ac)] / 2a. Be careful - the +/- means you have to find the answers for both addition as subtract, so that two answers are possible for these types of exercises.
   • An example: solving the quadratic formula 3x + 2x -1 = 0.

     x = [- b +/- √ (b - 4ac)] / 2a

     x = [- 2 +/- √ (2 - 4 (3) (- 1))] / 2 (3)

     x = [- 2 +/- √ (4 - (-12))] / 6

     x = [- 2 +/- √ (16)] / 6

     x = [- 2 +/- 4] / 6

     x =-1 and 1/3

4. Experiment with a system of equations. Solving multiple equations at the same time may sound tricky, but when you're working with simple algebraic equations, it's not that difficult. Math teachers often use a graph to solve these problems. If you work with systems of two equations, you will find the solution by looking at the points on the graph, where the lines of both equations intersect.
   • For example, suppose we are dealing with a system of the equations y = 3x - 2 and y = -x - 6. If we draw these two lines in a graph, we get a line that goes up steeply and one that goes less. goes down steeply. Because these lines intersect at the point (-1,-5), that is the solution of the system.
   • To check this, incorporate the answer into the equations of the system - a correct answer should "work" for both equations.

     y = 3x - 2

     -5=3(-1) - 2

     -5=-3 - 2

     -5=-5

     y = -x - 6

     -5=-(-1) - 6

     -5=1 - 6

     -5=-5

   • Both equations are "correct", so our answer is correct!

Tips

• There are tons of resources for people who want to learn algebra online. Just a simple search in a search engine like "algebra help" can give you dozens of great results. Also check out the Math category of wikiHow. There you will find a lot of information, so get started right away!
• A great site for algebra beginners is khanacademy.com. This free site offers loads of easy-to-follow lessons on a huge range of topics, including algebra. There are videos on everything from extremely simple to university level topics, so don't hesitate to take advantage of Khan Academy and all the help this site can give you!
• Remember, the best resources for learning algebra are people you already know. Consult with friends or other students attending the same class if you need help with topics covered in class.