Finite Math Examples

∣ ∣ ∣ \frac{5 x + 20}{4} ∣ ∣ ∣ = 5

$| \frac{5 x + 20}{4} | = 5$

Step 1

Remove the absolute value term. This creates a

\pm

$\pm$ on the right side of the equation because

| x | = \pm x

$| x | = \pm x$ .

\frac{5 x + 20}{4} = \pm 5

$\frac{5 x + 20}{4} = \pm 5$

Step 2

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

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Step 2.1

First, use the positive value of the

\pm

$\pm$ to find the first solution.

\frac{5 x + 20}{4} = 5

$\frac{5 x + 20}{4} = 5$

Step 2.2

Multiply both sides by

4

$4$ .

\frac{5 x + 20}{4} \cdot 4 = 5 \cdot 4

$\frac{5 x + 20}{4} \cdot 4 = 5 \cdot 4$

Step 2.3

Simplify.

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Step 2.3.1

Simplify the left side.

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Step 2.3.1.1

Simplify

\frac{5 x + 20}{4} \cdot 4

$\frac{5 x + 20}{4} \cdot 4$ .

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Step 2.3.1.1.1

Factor

5

$5$ out of

5 x + 20

$5 x + 20$ .

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Step 2.3.1.1.1.1

Factor

5

$5$ out of

5 x

$5 x$ .

\frac{5 (x) + 20}{4} \cdot 4 = 5 \cdot 4

$\frac{5 (x) + 20}{4} \cdot 4 = 5 \cdot 4$

Step 2.3.1.1.1.2

Factor

5

$5$ out of

20

$20$ .

\frac{5 x + 5 \cdot 4}{4} \cdot 4 = 5 \cdot 4

$\frac{5 x + 5 \cdot 4}{4} \cdot 4 = 5 \cdot 4$

Step 2.3.1.1.1.3

Factor

5

$5$ out of

5 x + 5 \cdot 4

$5 x + 5 \cdot 4$ .

\frac{5 (x + 4)}{4} \cdot 4 = 5 \cdot 4

$\frac{5 (x + 4)}{4} \cdot 4 = 5 \cdot 4$

\frac{5 (x + 4)}{4} \cdot 4 = 5 \cdot 4

$\frac{5 (x + 4)}{4} \cdot 4 = 5 \cdot 4$

Step 2.3.1.1.2

Cancel the common factor of

4

$4$ .

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Step 2.3.1.1.2.1

Cancel the common factor.

$\frac{5 (x + 4)}{4} \cdot 4 = 5 \cdot 4$

Step 2.3.1.1.2.2

Rewrite the expression.

$5 (x + 4) = 5 \cdot 4$

Step 2.3.1.1.3

Apply the distributive property.

$5 x + 5 \cdot 4 = 5 \cdot 4$

Step 2.3.1.1.4

Multiply

$5$ by

$4$ .

$5 x + 20 = 5 \cdot 4$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Multiply

$5$ by

$4$ .

$5 x + 20 = 20$

Step 2.4

Solve for

$x$ .

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Step 2.4.1

Move all terms not containing

$x$ to the right side of the equation.

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Step 2.4.1.1

Subtract

$20$ from both sides of the equation.

$5 x = 20 - 20$

Step 2.4.1.2

Subtract

$20$ from

$20$ .

$5 x = 0$

Step 2.4.2

Divide each term in

$5 x = 0$ by

$5$ and simplify.

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Step 2.4.2.1

Divide each term in

$5 x = 0$ by

$5$ .

$\frac{5 x}{5} = \frac{0}{5}$

Step 2.4.2.2

Simplify the left side.

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Step 2.4.2.2.1

Cancel the common factor of

$5$ .

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Step 2.4.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{0}{5}$

Step 2.4.2.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{0}{5}$

Step 2.4.2.3

Simplify the right side.

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Step 2.4.2.3.1

Divide

$0$ by

$5$ .

$x = 0$

Step 2.5

Next, use the negative value of the

$\pm$ to find the second solution.

$\frac{5 x + 20}{4} = - 5$

Step 2.6

Multiply both sides by

$4$ .

$\frac{5 x + 20}{4} \cdot 4 = - 5 \cdot 4$

Step 2.7

Simplify.

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Step 2.7.1

Simplify the left side.

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Step 2.7.1.1

Simplify

$\frac{5 x + 20}{4} \cdot 4$ .

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Step 2.7.1.1.1

Factor

$5$ out of

$5 x + 20$ .

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Step 2.7.1.1.1.1

Factor

$5$ out of

$5 x$ .

$\frac{5 (x) + 20}{4} \cdot 4 = - 5 \cdot 4$

Step 2.7.1.1.1.2

Factor

$5$ out of

$20$ .

$\frac{5 x + 5 \cdot 4}{4} \cdot 4 = - 5 \cdot 4$

Step 2.7.1.1.1.3

Factor

$5$ out of

$5 x + 5 \cdot 4$ .

$\frac{5 (x + 4)}{4} \cdot 4 = - 5 \cdot 4$

Step 2.7.1.1.2

Cancel the common factor of

$4$ .

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Step 2.7.1.1.2.1

Cancel the common factor.

$\frac{5 (x + 4)}{4} \cdot 4 = - 5 \cdot 4$

Step 2.7.1.1.2.2

Rewrite the expression.

$5 (x + 4) = - 5 \cdot 4$

Step 2.7.1.1.3

Apply the distributive property.

$5 x + 5 \cdot 4 = - 5 \cdot 4$

Step 2.7.1.1.4

Multiply

$5$ by

$4$ .

$5 x + 20 = - 5 \cdot 4$

Step 2.7.2

Simplify the right side.

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Step 2.7.2.1

Multiply

$- 5$ by

$4$ .

$5 x + 20 = - 20$

Step 2.8

Solve for

$x$ .

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Step 2.8.1

Move all terms not containing

$x$ to the right side of the equation.

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Step 2.8.1.1

Subtract

$20$ from both sides of the equation.

$5 x = - 20 - 20$

Step 2.8.1.2

Subtract

$20$ from

$- 20$ .

$5 x = - 40$

Step 2.8.2

Divide each term in

$5 x = - 40$ by

$5$ and simplify.

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Step 2.8.2.1

Divide each term in

$5 x = - 40$ by

$5$ .

$\frac{5 x}{5} = \frac{- 40}{5}$

Step 2.8.2.2

Simplify the left side.

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Step 2.8.2.2.1

Cancel the common factor of

$5$ .

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Step 2.8.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 40}{5}$

Step 2.8.2.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{- 40}{5}$

Step 2.8.2.3

Simplify the right side.

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Step 2.8.2.3.1

Divide

$- 40$ by

$5$ .

$x = - 8$

Step 2.9

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

$x = 0, - 8$