Algebra Examples

$| \frac{4 c}{5} + 6 | - 6 = - 5$

Step 1

Move all terms not containing $| \frac{4 c}{5} + 6 |$ to the right side of the equation.

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Step 1.1

Add $6$ to both sides of the equation.

$| \frac{4 c}{5} + 6 | = - 5 + 6$

Step 1.2

Add $- 5$ and $6$ .

$| \frac{4 c}{5} + 6 | = 1$

Step 2

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

$\frac{4 c}{5} + 6 = \pm 1$

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.

$\frac{4 c}{5} + 6 = 1$

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 $6$ from both sides of the equation.

$\frac{4 c}{5} = 1 - 6$

Step 3.2.2

Subtract $6$ from $1$ .

$\frac{4 c}{5} = - 5$

Step 3.3

Multiply both sides of the equation by $\frac{5}{4}$ .

$\frac{5}{4} \cdot \frac{4 c}{5} = \frac{5}{4} \cdot - 5$

Step 3.4

Simplify both sides of the equation.

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Step 3.4.1

Simplify the left side.

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Step 3.4.1.1

Simplify $\frac{5}{4} \cdot \frac{4 c}{5}$ .

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Step 3.4.1.1.1

Cancel the common factor of $5$ .

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Step 3.4.1.1.1.1

Cancel the common factor.

$\frac{5}{4} \cdot \frac{4 c}{5} = \frac{5}{4} \cdot - 5$

Step 3.4.1.1.1.2

Rewrite the expression.

$\frac{1}{4} (4 c) = \frac{5}{4} \cdot - 5$

Step 3.4.1.1.2

Cancel the common factor of $4$ .

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Step 3.4.1.1.2.1

Factor $4$ out of $4 c$ .

$\frac{1}{4} (4 (c)) = \frac{5}{4} \cdot - 5$

Step 3.4.1.1.2.2

Cancel the common factor.

$\frac{1}{4} (4 c) = \frac{5}{4} \cdot - 5$

Step 3.4.1.1.2.3

Rewrite the expression.

$c = \frac{5}{4} \cdot - 5$

Step 3.4.2

Simplify the right side.

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Step 3.4.2.1

Simplify $\frac{5}{4} \cdot - 5$ .

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Step 3.4.2.1.1

Multiply $\frac{5}{4} \cdot - 5$ .

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Step 3.4.2.1.1.1

Combine $\frac{5}{4}$ and $- 5$ .

$c = \frac{5 \cdot - 5}{4}$

Step 3.4.2.1.1.2

Multiply $5$ by $- 5$ .

$c = \frac{- 25}{4}$

Step 3.4.2.1.2

Move the negative in front of the fraction.

$c = - \frac{25}{4}$

Step 3.5

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

$\frac{4 c}{5} + 6 = - 1$

Step 3.6

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

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Step 3.6.1

Subtract $6$ from both sides of the equation.

$\frac{4 c}{5} = - 1 - 6$

Step 3.6.2

Subtract $6$ from $- 1$ .

$\frac{4 c}{5} = - 7$

Step 3.7

Multiply both sides of the equation by $\frac{5}{4}$ .

$\frac{5}{4} \cdot \frac{4 c}{5} = \frac{5}{4} \cdot - 7$

Step 3.8

Simplify both sides of the equation.

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Step 3.8.1

Simplify the left side.

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Step 3.8.1.1

Simplify $\frac{5}{4} \cdot \frac{4 c}{5}$ .

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Step 3.8.1.1.1

Cancel the common factor of $5$ .

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Step 3.8.1.1.1.1

Cancel the common factor.

$\frac{5}{4} \cdot \frac{4 c}{5} = \frac{5}{4} \cdot - 7$

Step 3.8.1.1.1.2

Rewrite the expression.

$\frac{1}{4} (4 c) = \frac{5}{4} \cdot - 7$

Step 3.8.1.1.2

Cancel the common factor of $4$ .

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Step 3.8.1.1.2.1

Factor $4$ out of $4 c$ .

$\frac{1}{4} (4 (c)) = \frac{5}{4} \cdot - 7$

Step 3.8.1.1.2.2

Cancel the common factor.

$\frac{1}{4} (4 c) = \frac{5}{4} \cdot - 7$

Step 3.8.1.1.2.3

Rewrite the expression.

$c = \frac{5}{4} \cdot - 7$

Step 3.8.2

Simplify the right side.

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Step 3.8.2.1

Simplify $\frac{5}{4} \cdot - 7$ .

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Step 3.8.2.1.1

Multiply $\frac{5}{4} \cdot - 7$ .

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Step 3.8.2.1.1.1

Combine $\frac{5}{4}$ and $- 7$ .

$c = \frac{5 \cdot - 7}{4}$

Step 3.8.2.1.1.2

Multiply $5$ by $- 7$ .

$c = \frac{- 35}{4}$

Step 3.8.2.1.2

Move the negative in front of the fraction.

$c = - \frac{35}{4}$

Step 3.9

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

$c = - \frac{25}{4}, - \frac{35}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$c = - \frac{25}{4}, - \frac{35}{4}$

Decimal Form:

$c = - 6.25, - 8.75$

Mixed Number Form:

$c = - 6 \frac{1}{4}, - 8 \frac{3}{4}$