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There are many methods to find the unknown x whether you are calculating the exponent, root, or just multiplying and dividing. Either way, you always have to find a way to put the unknown x on one side of the equation to find their value. Here’s how:
Steps
Using the basic linear equation
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Write the calculation like this:
- 2 2 (x+3) + 9 – 5 = 32
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Calculate exponentiation. Remember the order of the steps: In brackets, exponentiation, multiply/divide, add/subtract. You cannot do the calculation in brackets because it contains the unknown x, so you have to calculate the power first: 2 2 . 2 2 = 4
- 4(x+3) + 9 – 5 = 32
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Perform multiplication. [1] X Research Source Just multiply 4 by the numbers in brackets (x +3). Here’s how to do it:
- 4x + 12 + 9 – 5 = 32
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Perform addition and subtraction operations. 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
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Separate variables. [2] X Research Source To do this, you just need to divide both 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
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Check the results again. [3] X Research Source Just insert the value x = 4 back into the original equation to check. Here’s how to do it:
- 2 2 (x+3)+ 9 – 5 = 32
- 2 2 (4+3)+ 9 – 5 = 32
- 2 2 (7) + 9 – 5 = 32
- 4(7) + 9 – 5 = 32
- 28 + 9 – 5 = 32
- 37 – 5 = 32
- 32 = 32
Equations with caret
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Write calculations. Suppose you are solving a problem where the unknown x has a caret:
- 2x 2 + 12 = 44
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Split the term with the caret. [4] X Research Source The first thing to do is group the terms together so that the constants move to the right side of the equation while the exponent term is on the left side. Just subtract 12 on both sides. Here’s how to do it:
- 2x 2 +12-12 = 44-12
- 2x 2 = 32
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Split the variable with the caret by dividing both sides by the coefficient of the term containing x. In this case, 2 is the coefficient of x, so divide both sides of the equation by 2 to eliminate this number. Here’s how to do it:
- (2x 2 )/2 = 32/2
- x 2 = 16
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Calculate the square root of each side of the equation. [5] X Research Source Calculating the square root of x 2 will lose the caret. So let’s root both sides of the equation. You get x on one side and the square root of 16 as 4 on the other side. Thus, we have x = 4.
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Check the results again. Insert the value of x = 4 back into the original equation to check. Here’s how to do it:
- 2x 2 + 12 = 44
- 2 x (4) 2 + 12 = 44
- 2 x 16 + 12 = 44
- 32 + 12 = 44
- 44 = 44
Equations containing fractions
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Write calculations. Suppose you are solving the following problem: [6] X Research Source
- (x + 3)/6 = 2/3
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Cross multiply . To cross multiply, you simply multiply the denominator of one fraction by the numerator of the other. Basically, you multiply by two diagonals. Multiply 6, the denominator of the first fraction, by 2, the numerator of the second, and we get 12 on the right hand side of the equation. Multiply 3, the denominator of the second fraction, by x + 3, the numerator of the first fraction, and we get 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
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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
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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 of x. 3x/3 = x and 3/3 = 1, so you get the solution x = 1.
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Check the results again. To check, you just need to fit the x solution back into the original equation to make sure the result is correct. You will do the following:
- (x + 3)/6 = 2/3
- (1 + 3)/6 = 2/3
- 4/6 = 2/3
- 2/3 = 2/3
Equations with radical sign
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Write calculations. Suppose you have to find x in the following problem: [7] X Research Source
- (2x+9) – 5 = 0
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Split the square root. You must shift the part of the 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
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Square both sides. In the same way that you divide both sides of the equation by the coefficient, which is the number multiplied by x, you will square both sides of the equation if x is in the square root, or under the radical sign. This will remove the radical sign from the equation. You will do the following:
- (√(2x+9)) 2 = 5 2
- 2x + 9 = 25
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Group the same terms. Group the same 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
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Separate the variable. The last thing to do to find x is to isolate 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.
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Check the results again. 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
The equation contains the absolute value
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Write calculations. Suppose you want to find x in the following problem: [8] X Research Source
- |4x +2| – 6 = 8
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Separate absolute values. The first thing to do is to group the same terms and move the term inside the sign of the absolute value 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
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Drop 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 will be as follows:
- 4x + 2 = 14
- 4x + 2 – 2 = 14 -2
- 4x = 12
- x = 3
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Remove the absolute value and change the sign of the term beyond the equal sign before solving the problem. Now do it again, except change the sign of one side of the 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
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Check the results again. 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
Advice
- Square root is another expression of exponentiation. Square root of x = x^1/2.
- To check the result, substitute the value of x in the original equation and solve.
X
wikiHow is a “wiki” site, which means that many of the articles here are written by multiple authors. To create this article, 10 people, some of whom are anonymous, have edited and improved the article over time.
This article has been viewed 41,421 times.
There are many methods to find the unknown x whether you are calculating the exponent, root, or just multiplying and dividing. Either way, you always have to find a way to put the unknown x on one side of the equation to find their value. Here’s how:
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