Solve for h |(5h+2)/6|=7

$| \frac{5 h + 2}{6} | = 7$

Step 1

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

$\frac{5 h + 2}{6} = \pm 7$

Step 2

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.

$\frac{5 h + 2}{6} = 7$

Multiply both sides by $6$ .

$\frac{5 h + 2}{6} \cdot 6 = 7 \cdot 6$

Simplify.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{5 h + 2}{6} \cdot 6 = 7 \cdot 6$

Rewrite the expression.

$5 h + 2 = 7 \cdot 6$

Simplify the right side.

Multiply $7$ by $6$ .

$5 h + 2 = 42$

Solve for $h$ .

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

Subtract $2$ from both sides of the equation.

$5 h = 42 - 2$

Subtract $2$ from $42$ .

$5 h = 40$

Divide each term in $5 h = 40$ by $5$ and simplify.

Divide each term in $5 h = 40$ by $5$ .

$\frac{5 h}{5} = \frac{40}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 h}{5} = \frac{40}{5}$

Divide $h$ by $1$ .

$h = \frac{40}{5}$

Simplify the right side.

Divide $40$ by $5$ .

$h = 8$

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

$\frac{5 h + 2}{6} = - 7$

Multiply both sides by $6$ .

$\frac{5 h + 2}{6} \cdot 6 = - 7 \cdot 6$

Simplify.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{5 h + 2}{6} \cdot 6 = - 7 \cdot 6$

Rewrite the expression.

$5 h + 2 = - 7 \cdot 6$

Simplify the right side.

Multiply $- 7$ by $6$ .

$5 h + 2 = - 42$

Solve for $h$ .

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

Subtract $2$ from both sides of the equation.

$5 h = - 42 - 2$

Subtract $2$ from $- 42$ .

$5 h = - 44$

Divide each term in $5 h = - 44$ by $5$ and simplify.

Divide each term in $5 h = - 44$ by $5$ .

$\frac{5 h}{5} = \frac{- 44}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 h}{5} = \frac{- 44}{5}$

Divide $h$ by $1$ .

$h = \frac{- 44}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$h = - \frac{44}{5}$

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

$h = 8, - \frac{44}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$h = 8, - \frac{44}{5}$

Decimal Form:

$h = 8, - 8.8$

Mixed Number Form:

$h = 8, - 8 \frac{4}{5}$

Solve for h |(5h+2)/6|=7

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