Basic Math Examples

∣ ∣ \frac{y}{5} ∣ ∣ = 7

$| \frac{y}{5} | = 7$

Step 1

Remove the absolute value term. This creates a

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

$| x | = \pm x$ .

$\frac{y}{5} = \pm 7$

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

$\pm$ to find the first solution.

$\frac{y}{5} = 7$

Step 2.2

Multiply both sides of the equation by

$5$ .

$5 \frac{y}{5} = 5 \cdot 7$

Step 2.3

Simplify both sides of the equation.

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Step 2.3.1

Simplify the left side.

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Step 2.3.1.1

Cancel the common factor of

$5$ .

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Step 2.3.1.1.1

Cancel the common factor.

$5 \frac{y}{5} = 5 \cdot 7$

Step 2.3.1.1.2

Rewrite the expression.

$y = 5 \cdot 7$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Multiply

$5$ by

$7$ .

$y = 35$

Step 2.4

Next, use the negative value of the

$\pm$ to find the second solution.

$\frac{y}{5} = - 7$

Step 2.5

Multiply both sides of the equation by

$5$ .

$5 \frac{y}{5} = 5 \cdot - 7$

Step 2.6

Simplify both sides of the equation.

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Step 2.6.1

Simplify the left side.

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Step 2.6.1.1

Cancel the common factor of

$5$ .

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Step 2.6.1.1.1

Cancel the common factor.

$5 \frac{y}{5} = 5 \cdot - 7$

Step 2.6.1.1.2

Rewrite the expression.

$y = 5 \cdot - 7$

Step 2.6.2

Simplify the right side.

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Step 2.6.2.1

Multiply

$5$ by

$- 7$ .

$y = - 35$

Step 2.7

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

$y = 35, - 35$