Solve the Absolute Value Inequality for c |-4c+15|=35

$| - 4 c + 15 | = 35$

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

$- 4 c + 15 = \pm 35$

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.

$- 4 c + 15 = 35$

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

Subtract $15$ from both sides of the equation.

$- 4 c = 35 - 15$

Subtract $15$ from $35$ .

$- 4 c = 20$

Divide each term in $- 4 c = 20$ by $- 4$ and simplify.

Divide each term in $- 4 c = 20$ by $- 4$ .

$\frac{- 4 c}{- 4} = \frac{20}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 c}{- 4} = \frac{20}{- 4}$

Divide $c$ by $1$ .

$c = \frac{20}{- 4}$

Simplify the right side.

Divide $20$ by $- 4$ .

$c = - 5$

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

$- 4 c + 15 = - 35$

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

Subtract $15$ from both sides of the equation.

$- 4 c = - 35 - 15$

Subtract $15$ from $- 35$ .

$- 4 c = - 50$

Divide each term in $- 4 c = - 50$ by $- 4$ and simplify.

Divide each term in $- 4 c = - 50$ by $- 4$ .

$\frac{- 4 c}{- 4} = \frac{- 50}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 c}{- 4} = \frac{- 50}{- 4}$

Divide $c$ by $1$ .

$c = \frac{- 50}{- 4}$

Simplify the right side.

Cancel the common factor of $- 50$ and $- 4$ .

Factor $- 2$ out of $- 50$ .

$c = \frac{- 2 (25)}{- 4}$

Cancel the common factors.

Factor $- 2$ out of $- 4$ .

$c = \frac{- 2 \cdot 25}{- 2 \cdot 2}$

Cancel the common factor.

$c = \frac{- 2 \cdot 25}{- 2 \cdot 2}$

Rewrite the expression.

$c = \frac{25}{2}$

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

$c = - 5, \frac{25}{2}$

The result can be shown in multiple forms.

Exact Form:

$c = - 5, \frac{25}{2}$

Decimal Form:

$c = - 5, 12.5$

Mixed Number Form:

$c = - 5, 12 \frac{1}{2}$

Solve the Absolute Value Inequality for c |-4c+15|=35

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