Solve for m 4+|7-m|=5

$4 + | 7 - m | = 5$

Move all terms not containing $| 7 - m |$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$| 7 - m | = 5 - 4$

Subtract $4$ from $5$ .

$| 7 - m | = 1$

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$7 - m = \pm 1$

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

First, use the positive value of the $\pm$ to find the first solution.

$7 - m = 1$

Move all terms not containing $m$ to the right side of the equation.

Subtract $7$ from both sides of the equation.

$- m = 1 - 7$

Subtract $7$ from $1$ .

$- m = - 6$

Divide each term in $- m = - 6$ by $- 1$ and simplify.

Divide each term in $- m = - 6$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $m$ by $1$ .

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

Simplify the right side.

Divide $- 6$ by $- 1$ .

$m = 6$

Next, use the negative value of the $\pm$ to find the second solution.

$7 - m = - 1$

Move all terms not containing $m$ to the right side of the equation.

Subtract $7$ from both sides of the equation.

$- m = - 1 - 7$

Subtract $7$ from $- 1$ .

$- m = - 8$

Divide each term in $- m = - 8$ by $- 1$ and simplify.

Divide each term in $- m = - 8$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $m$ by $1$ .

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

Simplify the right side.

Divide $- 8$ by $- 1$ .

$m = 8$

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

$m = 6, 8$

Solve for m 4+|7-m|=5

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