Pre-Algebra Examples

$| 4 + 4 c | - 9 = - 7$

Step 1

Move all terms not containing $| 4 + 4 c |$ to the right side of the equation.

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Step 1.1

Add $9$ to both sides of the equation.

$| 4 + 4 c | = - 7 + 9$

Step 1.2

Add $- 7$ and $9$ .

$| 4 + 4 c | = 2$

Step 2

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

$4 + 4 c = \pm 2$

Step 3

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

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Step 3.1

First, use the positive value of the $\pm$ to find the first solution.

$4 + 4 c = 2$

Step 3.2

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

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Step 3.2.1

Subtract $4$ from both sides of the equation.

$4 c = 2 - 4$

Step 3.2.2

Subtract $4$ from $2$ .

$4 c = - 2$

Step 3.3

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

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Step 3.3.1

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

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

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $4$ .

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Step 3.3.2.1.1

Cancel the common factor.

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

Step 3.3.2.1.2

Divide $c$ by $1$ .

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

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

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

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Step 3.3.3.1.1

Factor $2$ out of $- 2$ .

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

Step 3.3.3.1.2

Cancel the common factors.

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Step 3.3.3.1.2.1

Factor $2$ out of $4$ .

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

Step 3.3.3.1.2.2

Cancel the common factor.

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

Step 3.3.3.1.2.3

Rewrite the expression.

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

Step 3.3.3.2

Move the negative in front of the fraction.

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

Step 3.4

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

$4 + 4 c = - 2$

Step 3.5

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

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Step 3.5.1

Subtract $4$ from both sides of the equation.

$4 c = - 2 - 4$

Step 3.5.2

Subtract $4$ from $- 2$ .

$4 c = - 6$

Step 3.6

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

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Step 3.6.1

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

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

Step 3.6.2

Simplify the left side.

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Step 3.6.2.1

Cancel the common factor of $4$ .

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Step 3.6.2.1.1

Cancel the common factor.

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

Step 3.6.2.1.2

Divide $c$ by $1$ .

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

Step 3.6.3

Simplify the right side.

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Step 3.6.3.1

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

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Step 3.6.3.1.1

Factor $2$ out of $- 6$ .

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

Step 3.6.3.1.2

Cancel the common factors.

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Step 3.6.3.1.2.1

Factor $2$ out of $4$ .

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

Step 3.6.3.1.2.2

Cancel the common factor.

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

Step 3.6.3.1.2.3

Rewrite the expression.

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

Step 3.6.3.2

Move the negative in front of the fraction.

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

Step 3.7

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

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