Algebra Examples

$4 + | 7 - m | = 5$

Step 1

Move all terms not containing

$| 7 - m |$ to the right side of the equation.

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Step 1.1

Subtract

$4$ from both sides of the equation.

$| 7 - m | = 5 - 4$

Step 1.2

Subtract

$4$ from

$5$ .

$| 7 - m | = 1$

Step 2

Remove the absolute value term. This creates a

$\pm$ on the right side of the equation because

$| x | = \pm x$ .

$7 - m = \pm 1$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.1

First, use the positive value of the

$\pm$ to find the first solution.

$7 - m = 1$

Step 3.2

Move all terms not containing

$m$ to the right side of the equation.

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Step 3.2.1

Subtract

$7$ from both sides of the equation.

$- m = 1 - 7$

Step 3.2.2

Subtract

$7$ from

$1$ .

$- m = - 6$

Step 3.3

Divide each term in

$- m = - 6$ by

$- 1$ and simplify.

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Step 3.3.1

Divide each term in

$- m = - 6$ by

$- 1$ .

$\frac{- m}{- 1} = \frac{- 6}{- 1}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Dividing two negative values results in a positive value.

$\frac{m}{1} = \frac{- 6}{- 1}$

Step 3.3.2.2

Divide

$m$ by

$1$ .

$m = \frac{- 6}{- 1}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide

$- 6$ by

$- 1$ .

$m = 6$

Step 3.4

Next, use the negative value of the

$\pm$ to find the second solution.

$7 - m = - 1$

Step 3.5

Move all terms not containing

$m$ to the right side of the equation.

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Step 3.5.1

Subtract

$7$ from both sides of the equation.

$- m = - 1 - 7$

Step 3.5.2

Subtract

$7$ from

$- 1$ .

$- m = - 8$

Step 3.6

Divide each term in

$- m = - 8$ by

$- 1$ and simplify.

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Step 3.6.1

Divide each term in

$- m = - 8$ by

$- 1$ .

$\frac{- m}{- 1} = \frac{- 8}{- 1}$

Step 3.6.2

Simplify the left side.

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Step 3.6.2.1

Dividing two negative values results in a positive value.

$\frac{m}{1} = \frac{- 8}{- 1}$

Step 3.6.2.2

Divide

$m$ by

$1$ .

$m = \frac{- 8}{- 1}$

Step 3.6.3

Simplify the right side.

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Step 3.6.3.1

Divide

$- 8$ by

$- 1$ .

$m = 8$

Step 3.7

The complete solution is the result of both the positive and negative portions of the solution.

$m = 6, 8$