Solve the Absolute Value Inequality for c |4c+2|=4

$| 4 c + 2 | = 4$

Step 1

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

$4 c + 2 = \pm 4$

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.

$4 c + 2 = 4$

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

Subtract $2$ from both sides of the equation.

$4 c = 4 - 2$

Subtract $2$ from $4$ .

$4 c = 2$

Divide each term in $4 c = 2$ by $4$ and simplify.

Divide each term in $4 c = 2$ by $4$ .

$\frac{4 c}{4} = \frac{2}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 c}{4} = \frac{2}{4}$

Divide $c$ by $1$ .

$c = \frac{2}{4}$

Simplify the right side.

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

$c = \frac{2 (1)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$c = \frac{2 \cdot 1}{2 \cdot 2}$

Cancel the common factor.

$c = \frac{2 \cdot 1}{2 \cdot 2}$

Rewrite the expression.

$c = \frac{1}{2}$

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

$4 c + 2 = - 4$

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

Subtract $2$ from both sides of the equation.

$4 c = - 4 - 2$

Subtract $2$ from $- 4$ .

$4 c = - 6$

Divide each term in $4 c = - 6$ by $4$ and simplify.

Divide each term in $4 c = - 6$ by $4$ .

$\frac{4 c}{4} = \frac{- 6}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 c}{4} = \frac{- 6}{4}$

Divide $c$ by $1$ .

$c = \frac{- 6}{4}$

Simplify the right side.

Cancel the common factor of $- 6$ and $4$ .

Factor $2$ out of $- 6$ .

$c = \frac{2 (- 3)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$c = \frac{2 \cdot - 3}{2 \cdot 2}$

Cancel the common factor.

$c = \frac{2 \cdot - 3}{2 \cdot 2}$

Rewrite the expression.

$c = \frac{- 3}{2}$

Move the negative in front of the fraction.

$c = - \frac{3}{2}$

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

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$c = 0.5, - 1.5$

Mixed Number Form:

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

Solve the Absolute Value Inequality for c |4c+2|=4

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