Basic Math Examples

$| 3 + 3 y | = 21$

Step 1

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

$3 + 3 y = \pm 21$

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.

$3 + 3 y = 21$

Step 2.2

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

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Step 2.2.1

Subtract $3$ from both sides of the equation.

$3 y = 21 - 3$

Step 2.2.2

Subtract $3$ from $21$ .

$3 y = 18$

Step 2.3

Divide each term in $3 y = 18$ by $3$ and simplify.

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Step 2.3.1

Divide each term in $3 y = 18$ by $3$ .

$\frac{3 y}{3} = \frac{18}{3}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $3$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{18}{3}$

Step 2.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{18}{3}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $18$ by $3$ .

$y = 6$

Step 2.4

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

$3 + 3 y = - 21$

Step 2.5

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

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Step 2.5.1

Subtract $3$ from both sides of the equation.

$3 y = - 21 - 3$

Step 2.5.2

Subtract $3$ from $- 21$ .

$3 y = - 24$

Step 2.6

Divide each term in $3 y = - 24$ by $3$ and simplify.

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Step 2.6.1

Divide each term in $3 y = - 24$ by $3$ .

$\frac{3 y}{3} = \frac{- 24}{3}$

Step 2.6.2

Simplify the left side.

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Step 2.6.2.1

Cancel the common factor of $3$ .

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Step 2.6.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 24}{3}$

Step 2.6.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 24}{3}$

Step 2.6.3

Simplify the right side.

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Step 2.6.3.1

Divide $- 24$ by $3$ .

$y = - 8$

Step 2.7

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

$y = 6, - 8$