Basic Math Examples

- 8 + ∣ ∣ ∣ \frac{1}{3} a ∣ ∣ ∣ = - 5

$- 8 + | \frac{1}{3} a | = - 5$

Step 1

Move all terms not containing

∣ ∣ ∣ \frac{1}{3} a ∣ ∣ ∣

$| \frac{1}{3} a |$ to the right side of the equation.

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Step 1.1

Add

8

$8$ to both sides of the equation.

∣ ∣ ∣ \frac{1}{3} a ∣ ∣ ∣ = - 5 + 8

$| \frac{1}{3} a | = - 5 + 8$

Step 1.2

Add

- 5

$- 5$ and

8

$8$ .

∣ ∣ ∣ \frac{1}{3} a ∣ ∣ ∣ = 3

$| \frac{1}{3} a | = 3$

∣ ∣ ∣ \frac{1}{3} a ∣ ∣ ∣ = 3

$| \frac{1}{3} a | = 3$

Step 2

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{1}{3} a = \pm 3

$\frac{1}{3} a = \pm 3$

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

$\pm$ to find the first solution.

\frac{1}{3} a = 3

$\frac{1}{3} a = 3$

Step 3.2

Multiply both sides of the equation by

3

$3$ .

3 (\frac{1}{3} a) = 3 \cdot 3

$3 (\frac{1}{3} a) = 3 \cdot 3$

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Simplify

3 (\frac{1}{3} a)

$3 (\frac{1}{3} a)$ .

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Step 3.3.1.1.1

Combine

\frac{1}{3}

$\frac{1}{3}$ and

a

$a$ .

3 \frac{a}{3} = 3 \cdot 3

$3 \frac{a}{3} = 3 \cdot 3$

Step 3.3.1.1.2

Cancel the common factor of

3

$3$ .

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Step 3.3.1.1.2.1

Cancel the common factor.

$3 \frac{a}{3} = 3 \cdot 3$

Step 3.3.1.1.2.2

Rewrite the expression.

$a = 3 \cdot 3$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Multiply

$3$ by

$3$ .

$a = 9$

Step 3.4

Next, use the negative value of the

$\pm$ to find the second solution.

$\frac{1}{3} a = - 3$

Step 3.5

Multiply both sides of the equation by

$3$ .

$3 (\frac{1}{3} a) = 3 \cdot - 3$

Step 3.6

Simplify both sides of the equation.

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Step 3.6.1

Simplify the left side.

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Step 3.6.1.1

Simplify

$3 (\frac{1}{3} a)$ .

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Step 3.6.1.1.1

Combine

$\frac{1}{3}$ and

$a$ .

$3 \frac{a}{3} = 3 \cdot - 3$

Step 3.6.1.1.2

Cancel the common factor of

$3$ .

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Step 3.6.1.1.2.1

Cancel the common factor.

$3 \frac{a}{3} = 3 \cdot - 3$

Step 3.6.1.1.2.2

Rewrite the expression.

$a = 3 \cdot - 3$

Step 3.6.2

Simplify the right side.

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Step 3.6.2.1

Multiply

$3$ by

$- 3$ .

$a = - 9$

Step 3.7

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

$a = 9, - 9$