Content

• Steps
• Advice

There are many methods to find unknown x whether you are calculating an exponent, root, or just multiplying. Either way, you always have to find a way to bring the unknown x to one side of the equation in order to find their value. Here's how:

Steps

Method 1 of 5: Use basic linear equations

1. 

   Write the calculation like this:
   • 2 (x + 3) + 9 - 5 = 32

2. 

   
   
   Exponentiation. Remember the order of steps: In brackets, powers, multiplication / division, addition / subtraction. You cannot do the math in parentheses because it contains an unknown number of x, so you must calculate the power first: 2. 2 = 4
   • 4 (x + 3) + 9 - 5 = 32

3. 

   Perform multiplication calculations. Just multiply 4 by the numbers in parentheses (x +3). Here's how to do it:
   • 4x + 12 + 9 - 5 = 32

4. 

   
   
   Perform addition and subtraction calculations. Just add or subtract the remaining numbers. Here's how to do it:
   • 4x + 21-5 = 32
   • 4x + 16 = 32
   • 4x + 16 - 16 = 32 - 16
   • 4x = 16

5. 

   Separate the variables. To do this, simply divide the two sides of the equation by 4 to find x. 4x / 4 = x and 16/4 = 4, so x = 4.
   • 4x / 4 = 16/4
   • x = 4

6. 

   
   
   Check the results. Just fit x = 4 back to the original equation to test. Here's how to do it:
   • 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
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Method 2 of 5: Equation with caret

1. 

   Write the math. Let's say that you are solving a problem where x is hidden:
   • 2x + 12 = 44

2. 

   Separate the term with an exponent. The first thing to do is to group the same terms so that the constants move to the right side of the equation while the term has the exponent on the left. Just subtract 12 on both sides. Here's how to do it:
   • 2x + 12-12 = 44-12
   • 2x = 32

3. 

   Separate the exponent variable by dividing both sides by the coefficient of the term containing x. In this case, 2 is a coefficient of x, so divide both sides of the equation by 2 to remove this number. Here's how to do it:
   • (2x) / 2 = 32/2
   • x = 16

4. 

   Calculate the square root of each side of the equation. Calculating the square root of x takes the exponent away. So, let's root both sides of the equation. You will get x on one side and the square root of 16 to 4 on the other side. Thus, we have x = 4.

5. 

   Check the results. Reinsert x = 4 back to the original equation to test. Here's how to do it:
   • 2x + 12 = 44
   • 2 x (4) + 12 = 44
   • 2 x 16 + 12 = 44
   • 32 + 12 = 44
   • 44 = 44
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Method 3 of 5: Equations containing fractions

1. 

   Write the math. Let's say you are solving the following problem:
   • (x + 3) / 6 = 2/3

2. 

   Cross multiplication. To cross multiply, simply multiply the denominator of one fraction by the numerator of the other. Basically, you multiply it diagonally. Multiply 6, the denominator of the first fraction, and by 2, the numerator of the second fraction, get 12 on the right side of the equation. Multiplying 3, the denominator of the second fraction, by x + 3, the numerator of the first fraction, gives 3 x + 9 on the left side of the equation. Here's how to do it:
   • (x + 3) / 6 = 2/3
   • 6 x 2 = 12
   • (x + 3) x 3 = 3x + 9
   • 3x + 9 = 12

3. 

   Group the same terms. Group the constants in the equation by subtracting 9 from both sides of the equation. You will do the following:
   • 3x + 9 - 9 = 12 - 9
   • 3x = 3

4. 

   Split x by dividing each term by the coefficient of x. Divide 3x and 9 by 3, the coefficient of x to find the solution x. 3x / 3 = x and 3/3 = 1, so you will have solution x = 1.

5. 

   Check the results. To test it, simply put the solution x back in the original equation to ensure the correct results. You will do the following:
   • (x + 3) / 6 = 2/3
   • (1 + 3)/6 = 2/3
   • 4/6 = 2/3
   • 2/3 = 2/3
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Method 4 of 5: Equation with radical signs

1. 

   Write the math. Suppose you have to find x in the following problem:
   • √ (2x + 9) - 5 = 0

2. 

   Split the square root. You must move the part of an equation that contains the radical sign to one side before continuing. You will have to add 5 to both sides of the equation. Here's how to do it:
   • √ (2x + 9) - 5 + 5 = 0 + 5
   • √ (2x + 9) = 5

3. 

   Square both sides. In the same way that you divide both sides of the equation by coefficients, multiplied by x, you will square both sides of the equation if x is on the square root, or below the radical sign. This will remove the radical sign from the equation. You will do the following:
   • (√ (2x + 9)) = 5
   • 2x + 9 = 25

4. 

   Group the same terms. Group similar terms by subtracting both sides by 9 to move the constants to the right side of the equation, while x is on the left side. Here's how to do it:
   • 2x + 9 - 9 = 25 - 9
   • 2x = 16

5. 

   Separate the variables. The last thing to do to find x is to separate the variable by dividing both sides of the equation by 2, the coefficient of x. 2x / 2 = x and 16/2 = 8, you get the solution x = 8.

6. 

   Check the results. Insert 8 into the equation for x to see if the result is correct:
   • √ (2x + 9) - 5 = 0
   • √(2(8)+9) - 5 = 0
   • √(16+9) - 5 = 0
   • √(25) - 5 = 0
   • 5 - 5 = 0
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Method 5 of 5: Equation containing absolute value

1. 

   Write the math. Suppose you want to find x in the following problem:
   • | 4x +2 | - 6 = 8

2. 

   Separate absolute value. The first thing to do is to group the same terms and move the term inside the absolute value sign to one side. In this case, you would add 6 to both sides of the equation. Here's how to do it:
   • | 4x +2 | - 6 = 8
   • | 4x +2 | - 6 + 6 = 8 + 6
   • | 4x +2 | = 14

3. 

   Remove the absolute value and solve the equation. This is the first and simplest step. You will have to solve to find the solution x twice when the problem has absolute value. The first step would look like this:
   • 4x + 2 = 14
   • 4x + 2 - 2 = 14 -2
   • 4x = 12
   • x = 3

4. 

   Remove the absolute value and change the sign of the term beyond the equal sign before solving the problem. Now do it again, except to convert the one-sided equation to -14 instead of 14. Here's how:
   • 4x + 2 = -14
   • 4x + 2 - 2 = -14 - 2
   • 4x = -16
   • 4x / 4 = -16/4
   • x = -4

5. 

   Check the results. Now that you know the solution x = (3, -4), plug both numbers into the equation to check. Here's how to do it:
   • (With x = 3):
     • | 4x +2 | - 6 = 8
     • |4(3) +2| - 6 = 8
     • |12 +2| - 6 = 8
     • |14| - 6 = 8
     • 14 - 6 = 8
     • 8 = 8
   • (With x = -4):
     • | 4x +2 | - 6 = 8
     • |4(-4) +2| - 6 = 8
     • |-16 +2| - 6 = 8
     • |-14| - 6 = 8
     • 14 - 6 = 8
     • 8 = 8
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Advice

• Square root is another manifestation of power. Square root of x = x ^ 1/2.
• To check the result, replace the value of x in the original equation and solve.