Solve the Absolute Value Inequality for c 10=|-15+3c|

$10 = | - 15 + 3 c |$

Rewrite the equation as $| - 15 + 3 c | = 10$ .

$| - 15 + 3 c | = 10$

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

$- 15 + 3 c = \pm 10$

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.

$- 15 + 3 c = 10$

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

Add $15$ to both sides of the equation.

$3 c = 10 + 15$

Add $10$ and $15$ .

$3 c = 25$

Divide each term in $3 c = 25$ by $3$ and simplify.

Divide each term in $3 c = 25$ by $3$ .

$\frac{3 c}{3} = \frac{25}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 c}{3} = \frac{25}{3}$

Divide $c$ by $1$ .

$c = \frac{25}{3}$

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

$- 15 + 3 c = - 10$

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

Add $15$ to both sides of the equation.

$3 c = - 10 + 15$

Add $- 10$ and $15$ .

$3 c = 5$

Divide each term in $3 c = 5$ by $3$ and simplify.

Divide each term in $3 c = 5$ by $3$ .

$\frac{3 c}{3} = \frac{5}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 c}{3} = \frac{5}{3}$

Divide $c$ by $1$ .

$c = \frac{5}{3}$

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

$c = \frac{25}{3}, \frac{5}{3}$

The result can be shown in multiple forms.

Exact Form:

$c = \frac{25}{3}, \frac{5}{3}$

Decimal Form:

$c = 8.\overline{3}, 1.\overline{6}$

Mixed Number Form:

$c = 8 \frac{1}{3}, 1 \frac{2}{3}$

Solve the Absolute Value Inequality for c 10=|-15+3c|

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