Solve for x 10+|7-5x|=11

$10 + | 7 - 5 x | = 11$

Step 1

Move all terms not containing $| 7 - 5 x |$ to the right side of the equation.

Subtract $10$ from both sides of the equation.

$| 7 - 5 x | = 11 - 10$

Subtract $10$ from $11$ .

$| 7 - 5 x | = 1$

Step 2

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

$7 - 5 x = \pm 1$

Step 3

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.

$7 - 5 x = 1$

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

Subtract $7$ from both sides of the equation.

$- 5 x = 1 - 7$

Subtract $7$ from $1$ .

$- 5 x = - 6$

Divide each term in $- 5 x = - 6$ by $- 5$ and simplify.

Divide each term in $- 5 x = - 6$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 6}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 6}{- 5}$

Divide $x$ by $1$ .

$x = \frac{- 6}{- 5}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{6}{5}$

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

$7 - 5 x = - 1$

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

Subtract $7$ from both sides of the equation.

$- 5 x = - 1 - 7$

Subtract $7$ from $- 1$ .

$- 5 x = - 8$

Divide each term in $- 5 x = - 8$ by $- 5$ and simplify.

Divide each term in $- 5 x = - 8$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 8}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 8}{- 5}$

Divide $x$ by $1$ .

$x = \frac{- 8}{- 5}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{8}{5}$

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

$x = \frac{6}{5}, \frac{8}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{6}{5}, \frac{8}{5}$

Decimal Form:

$x = 1.2, 1.6$

Mixed Number Form:

$x = 1 \frac{1}{5}, 1 \frac{3}{5}$

Solve for x 10+|7-5x|=11

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