Content

• Steps
• Method 1 of 5: Solving Basic Linear Equations
• Method 2 of 5: With degrees
• Method 3 of 5: Solving Equations with Fractions
• Method 4 of 5: Solving Equations with Radicals
• Method 5 of 5: Solving Equations with Modules
• Tips

There are many ways to solve equations in one unknown. These equations can include powers and radicals, or simple division and multiplication operations. Whatever solution you use, you will need to find a way to isolate x on one side of the equation in order to find its value. Here's how to do it.

Steps

Method 1 of 5: Solving Basic Linear Equations

1. 1 Write an equation. For example:
   • 2 (x + 3) + 9 - 5 = 32
2. 2 Raise to the power. Remember the order of operations: S.E.U.D.P.V. (Look, These Craftsmen Make A Fluttering Bike), which stands for Brackets, Exponents, Multiplication, Division, Addition, Subtraction. You cannot first execute the parenthesized expressions because x is there. Therefore, you need to start with a degree: 2.2 = 4
   • 4 (x + 3) + 9 - 5 = 32
3. 3 Perform multiplication. Just distribute the factor 4 in the expression (x +3):
   • 4x + 12 + 9 - 5 = 32
4. 4 Perform addition and subtraction. Just add or subtract the remaining numbers:
   • 4x + 21-5 = 32
   • 4x + 16 = 32
   • 4x + 16 - 16 = 32 - 16
   • 4x = 16
5. 5 Isolate the variable. To do this, divide both sides of the equation by 4 to find x later. 4x / 4 = x and 16/4 = 4, so x = 4.
   • 4x / 4 = 16/4
   • x = 4
6. 6 Check the correctness of the solution. Just plug x = 4 into the original equation to make sure it converges:
   • 2 (x + 3) + 9 - 5 = 32
   • 2(4+3)+ 9 - 5 = 32
   • 2(7) + 9 - 5 = 32
   • 4(7) + 9 - 5 = 32
   • 28 + 9 - 5 = 32
   • 37 - 5 = 32
   • 32 = 32

Method 2 of 5: With degrees

1. 1 Write an equation. Let's say you need to solve an equation like this, where x is raised to a power:
   • 2x + 12 = 44
2. 2 Highlight the term with the degree. The first thing you need to do is concatenate similar terms so that all numerical values ​​are on the right side of the equation and the exponent term is on the left. Just subtract 12 from both sides of the equation:
   • 2x + 12-12 = 44-12
   • 2x = 32
3. 3 Isolate the unknown with a power by dividing both sides by the coefficient of x. In our case, we know that the coefficient at x is 2, so you need to divide both sides of the equation by 2 to get rid of it:
   • (2x) / 2 = 32/2
   • x = 16
4. 4 Take the square root of each equation. After extracting the square root of x, there is no need for a power with it. So, take the square root of both sides. You are left with x on the left and the square root of 16, 4 on the right. Therefore, x = 4.
5. 5 Check the correctness of the solution. Just plug x = 4 into the original equation to make sure it converges:
   • 2x + 12 = 44
   • 2 x (4) + 12 = 44
   • 2 x 16 + 12 = 44
   • 32 + 12 = 44
   • 44 = 44

Method 3 of 5: Solving Equations with Fractions

1. 1 Write an equation. For example, you came across this:
   • (x + 3) / 6 = 2/3
2. 2 Multiply crosswise. To multiply crosswise, simply multiply the denominator of each fraction by the numerator of the other. Basically, you will be multiplying along the diagonal lines. So, multiply the first denominator, 6, by the numerator of the second fraction, 2, and you get 12 on the right side of the equation. Multiply the second denominator, 3, by the first numerator, x + 3, to get 3 x + 9 on the left side of the equation. Here's what you get:
   • (x + 3) / 6 = 2/3
   • 6 x 2 = 12
   • (x + 3) x 3 = 3x + 9
   • 3x + 9 = 12
3. 3 Combine similar members. Combine the numbers in the equation by subtracting 9 from both sides:
   • 3x + 9 - 9 = 12 - 9
   • 3x = 3
4. 4 Isolate x by dividing each term by the coefficient of x. Just divide 3x and 9 by 3, the coefficient of x, to solve the equation. 3x / 3 = x and 3/3 = 1, so x = 1.
5. 5 Check the correctness of the solution. Just plug x into the original equation to make sure it converges:
   • (x + 3) / 6 = 2/3
   • (1 + 3)/6 = 2/3
   • 4/6 = 2/3
   • 2/3 = 2/3

Method 4 of 5: Solving Equations with Radicals

1. 1 Write an equation. Let's say you want to find x in the following equation:
   • √ (2x + 9) - 5 = 0
2. 2 Isolate the square root. Move the square root part of the equation to one side before continuing. To do this, add to both sides of Equation 5:
   • √ (2x + 9) - 5 + 5 = 0 + 5
   • √ (2x + 9) = 5
3. 3 Square both sides of the equation. Just as you would divide both sides of the equation by the coefficient at x, square both sides of the equation if x is at the square root (under the radical sign). This will eliminate the root sign from the equation:
   • (√ (2x + 9)) = 5
   • 2x + 9 = 25
4. 4 Combine similar members. Combine similar terms by subtracting 9 from both sides so that all numbers are on the right side of the equation and x is on the left:
   • 2x + 9 - 9 = 25 - 9
   • 2x = 16
5. 5 Isolate the unknown quantity. The last thing you need to do to find the value of x is to isolate the unknown by dividing both sides of the equation by 2, the coefficient of x. 2x / 2 = x and 16/2 = 8, so you get x = 8.
6. 6 Check the correctness of the solution. Just plug 8 into the original equation for x to make sure you get the correct answer:
   • √ (2x + 9) - 5 = 0
   • √(2(8)+9) - 5 = 0
   • √(16+9) - 5 = 0
   • √(25) - 5 = 0
   • 5 - 5 = 0

Method 5 of 5: Solving Equations with Modules

1. 1 Write an equation. Let's say you want to solve an equation like this:
   • | 4x +2 | - 6 = 8
2. 2 Isolate the absolute value. The first thing you need to do is concatenate similar terms to get an expression in a modulus on one side of the equation. In this case, you need to add 6 to both sides of the equation:
   • | 4x +2 | - 6 = 8
   • | 4x +2 | - 6 + 6 = 8 + 6
   • | 4x +2 | = 14
3. 3 Remove the module and solve the equation. This is the first and easiest step. When working with modules, you need to look for x twice. You need to do this the first time like this:
   • 4x + 2 = 14
   • 4x + 2 - 2 = 14 -2
   • 4x = 12
   • x = 3
4. 4 Remove the module and change the sign of the terms of the expression on the other side of the equal sign to the opposite, and only then start solving the equation. Now do everything as before, just make the first part of the equation equal to -14 instead of 14:
   • 4x + 2 = -14
   • 4x + 2 - 2 = -14 - 2
   • 4x = -16
   • 4x / 4 = -16/4
   • x = -4
5. 5 Check the correctness of the solution. Now, knowing that x = (3, -4), just plug both numbers into the equation and make sure you get the correct answer:
   • (For x = 3):
     • | 4x +2 | - 6 = 8
     • |4(3) +2| - 6 = 8
     • |12 +2| - 6 = 8
     • |14| - 6 = 8
     • 14 - 6 = 8
     • 8 = 8
   • (For x = -4):
     • | 4x +2 | - 6 = 8
     • |4(-4) +2| - 6 = 8
     • |-16 +2| - 6 = 8
     • |-14| - 6 = 8
     • 14 - 6 = 8
     • 8 = 8

Tips

• To check the correctness of the solution, plug the value of x into the original equation and calculate the resulting expression.
• Radicals or roots are a way of representing a degree. Square root x = x ^ 1/2.