Basic Math Examples

$\frac{| 6 y + 6 |}{6} = 3$

Step 1

Multiply both sides by $6$ .

$\frac{| 6 y + 6 |}{6} \cdot 6 = 3 \cdot 6$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{| 6 y + 6 |}{6} \cdot 6$ .

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Step 2.1.1.1

Simplify the numerator.

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Step 2.1.1.1.1

Factor $6$ out of $6 y + 6$ .

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Step 2.1.1.1.1.1

Factor $6$ out of $6 y$ .

$\frac{| 6 (y) + 6 |}{6} \cdot 6 = 3 \cdot 6$

Step 2.1.1.1.1.2

Factor $6$ out of $6$ .

$\frac{| 6 (y) + 6 (1) |}{6} \cdot 6 = 3 \cdot 6$

Step 2.1.1.1.1.3

Factor $6$ out of $6 (y) + 6 (1)$ .

$\frac{| 6 (y + 1) |}{6} \cdot 6 = 3 \cdot 6$

Step 2.1.1.1.2

Apply the distributive property.

$\frac{| 6 y + 6 \cdot 1 |}{6} \cdot 6 = 3 \cdot 6$

Step 2.1.1.1.3

Multiply $6$ by $1$ .

$\frac{| 6 y + 6 |}{6} \cdot 6 = 3 \cdot 6$

Step 2.1.1.1.4

Factor $6$ out of $6 y + 6$ .

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Step 2.1.1.1.4.1

Factor $6$ out of $6 y$ .

$\frac{| 6 (y) + 6 |}{6} \cdot 6 = 3 \cdot 6$

Step 2.1.1.1.4.2

Factor $6$ out of $6$ .

$\frac{| 6 (y) + 6 (1) |}{6} \cdot 6 = 3 \cdot 6$

Step 2.1.1.1.4.3

Factor $6$ out of $6 (y) + 6 (1)$ .

$\frac{| 6 (y + 1) |}{6} \cdot 6 = 3 \cdot 6$

Step 2.1.1.2

Remove non-negative terms from the absolute value.

$\frac{6 | y + 1 |}{6} \cdot 6 = 3 \cdot 6$

Step 2.1.1.3

Cancel the common factor of $6$ .

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Step 2.1.1.3.1

Cancel the common factor.

$\frac{6 | y + 1 |}{6} \cdot 6 = 3 \cdot 6$

Step 2.1.1.3.2

Rewrite the expression.

$6 | y + 1 | = 3 \cdot 6$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $3$ by $6$ .

$6 | y + 1 | = 18$

Step 3

Solve for $y$ .

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Step 3.1

Divide each term in $6 | y + 1 | = 18$ by $6$ and simplify.

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Step 3.1.1

Divide each term in $6 | y + 1 | = 18$ by $6$ .

$\frac{6 | y + 1 |}{6} = \frac{18}{6}$

Step 3.1.2

Simplify the left side.

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Step 3.1.2.1

Cancel the common factor of $6$ .

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Step 3.1.2.1.1

Cancel the common factor.

$\frac{6 | y + 1 |}{6} = \frac{18}{6}$

Step 3.1.2.1.2

Divide $| y + 1 |$ by $1$ .

$| y + 1 | = \frac{18}{6}$

Step 3.1.3

Simplify the right side.

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Step 3.1.3.1

Divide $18$ by $6$ .

$| y + 1 | = 3$

Step 3.2

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

$y + 1 = \pm 3$

Step 3.3

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

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Step 3.3.1

First, use the positive value of the $\pm$ to find the first solution.

$y + 1 = 3$

Step 3.3.2

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

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Step 3.3.2.1

Subtract $1$ from both sides of the equation.

$y = 3 - 1$

Step 3.3.2.2

Subtract $1$ from $3$ .

$y = 2$

Step 3.3.3

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

$y + 1 = - 3$

Step 3.3.4

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

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Step 3.3.4.1

Subtract $1$ from both sides of the equation.

$y = - 3 - 1$

Step 3.3.4.2

Subtract $1$ from $- 3$ .

$y = - 4$

Step 3.3.5

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

$y = 2, - 4$