Pre-Algebra Examples

$4 x + 12 y = 36$

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

$4 (- 2) + 12 y = 36$

Step 2

Solve the equation for $y$ .

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Step 2.1

Multiply $4$ by $- 2$ .

$- 8 + 12 y = 36$

Step 2.2

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

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Step 2.2.1

Add $8$ to both sides of the equation.

$12 y = 36 + 8$

Step 2.2.2

Add $36$ and $8$ .

$12 y = 44$

Step 2.3

Divide each term in $12 y = 44$ by $12$ and simplify.

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Step 2.3.1

Divide each term in $12 y = 44$ by $12$ .

$\frac{12 y}{12} = \frac{44}{12}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $12$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{12 y}{12} = \frac{44}{12}$

Step 2.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{44}{12}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Cancel the common factor of $44$ and $12$ .

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Step 2.3.3.1.1

Factor $4$ out of $44$ .

$y = \frac{4 (11)}{12}$

Step 2.3.3.1.2

Cancel the common factors.

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Step 2.3.3.1.2.1

Factor $4$ out of $12$ .

$y = \frac{4 \cdot 11}{4 \cdot 3}$

Step 2.3.3.1.2.2

Cancel the common factor.

$y = \frac{4 \cdot 11}{4 \cdot 3}$

Step 2.3.3.1.2.3

Rewrite the expression.

$y = \frac{11}{3}$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

$4 (- 1) + 12 y = 36$

Step 4

Solve the equation for $y$ .

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Step 4.1

Multiply $4$ by $- 1$ .

$- 4 + 12 y = 36$

Step 4.2

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

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Step 4.2.1

Add $4$ to both sides of the equation.

$12 y = 36 + 4$

Step 4.2.2

Add $36$ and $4$ .

$12 y = 40$

Step 4.3

Divide each term in $12 y = 40$ by $12$ and simplify.

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Step 4.3.1

Divide each term in $12 y = 40$ by $12$ .

$\frac{12 y}{12} = \frac{40}{12}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $12$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{12 y}{12} = \frac{40}{12}$

Step 4.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{40}{12}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Cancel the common factor of $40$ and $12$ .

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Step 4.3.3.1.1

Factor $4$ out of $40$ .

$y = \frac{4 (10)}{12}$

Step 4.3.3.1.2

Cancel the common factors.

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Step 4.3.3.1.2.1

Factor $4$ out of $12$ .

$y = \frac{4 \cdot 10}{4 \cdot 3}$

Step 4.3.3.1.2.2

Cancel the common factor.

$y = \frac{4 \cdot 10}{4 \cdot 3}$

Step 4.3.3.1.2.3

Rewrite the expression.

$y = \frac{10}{3}$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$4 (0) + 12 y = 36$

Step 6

Solve the equation for $y$ .

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Step 6.1

Simplify $4 (0) + 12 y$ .

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Step 6.1.1

Multiply $4$ by $0$ .

$0 + 12 y = 36$

Step 6.1.2

Add $0$ and $12 y$ .

$12 y = 36$

Step 6.2

Divide each term in $12 y = 36$ by $12$ and simplify.

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Step 6.2.1

Divide each term in $12 y = 36$ by $12$ .

$\frac{12 y}{12} = \frac{36}{12}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $12$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{12 y}{12} = \frac{36}{12}$

Step 6.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{36}{12}$

Step 6.2.3

Simplify the right side.

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Step 6.2.3.1

Divide $36$ by $12$ .

$y = 3$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

$4 (1) + 12 y = 36$

Step 8

Solve the equation for $y$ .

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Step 8.1

Multiply $4$ by $1$ .

$4 + 12 y = 36$

Step 8.2

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

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Step 8.2.1

Subtract $4$ from both sides of the equation.

$12 y = 36 - 4$

Step 8.2.2

Subtract $4$ from $36$ .

$12 y = 32$

Step 8.3

Divide each term in $12 y = 32$ by $12$ and simplify.

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Step 8.3.1

Divide each term in $12 y = 32$ by $12$ .

$\frac{12 y}{12} = \frac{32}{12}$

Step 8.3.2

Simplify the left side.

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Step 8.3.2.1

Cancel the common factor of $12$ .

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Step 8.3.2.1.1

Cancel the common factor.

$\frac{12 y}{12} = \frac{32}{12}$

Step 8.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{32}{12}$

Step 8.3.3

Simplify the right side.

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Step 8.3.3.1

Cancel the common factor of $32$ and $12$ .

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Step 8.3.3.1.1

Factor $4$ out of $32$ .

$y = \frac{4 (8)}{12}$

Step 8.3.3.1.2

Cancel the common factors.

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Step 8.3.3.1.2.1

Factor $4$ out of $12$ .

$y = \frac{4 \cdot 8}{4 \cdot 3}$

Step 8.3.3.1.2.2

Cancel the common factor.

$y = \frac{4 \cdot 8}{4 \cdot 3}$

Step 8.3.3.1.2.3

Rewrite the expression.

$y = \frac{8}{3}$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$4 (2) + 12 y = 36$

Step 10

Solve the equation for $y$ .

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Step 10.1

Multiply $4$ by $2$ .

$8 + 12 y = 36$

Step 10.2

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

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Step 10.2.1

Subtract $8$ from both sides of the equation.

$12 y = 36 - 8$

Step 10.2.2

Subtract $8$ from $36$ .

$12 y = 28$

Step 10.3

Divide each term in $12 y = 28$ by $12$ and simplify.

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Step 10.3.1

Divide each term in $12 y = 28$ by $12$ .

$\frac{12 y}{12} = \frac{28}{12}$

Step 10.3.2

Simplify the left side.

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Step 10.3.2.1

Cancel the common factor of $12$ .

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Step 10.3.2.1.1

Cancel the common factor.

$\frac{12 y}{12} = \frac{28}{12}$

Step 10.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{28}{12}$

Step 10.3.3

Simplify the right side.

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Step 10.3.3.1

Cancel the common factor of $28$ and $12$ .

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Step 10.3.3.1.1

Factor $4$ out of $28$ .

$y = \frac{4 (7)}{12}$

Step 10.3.3.1.2

Cancel the common factors.

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Step 10.3.3.1.2.1

Factor $4$ out of $12$ .

$y = \frac{4 \cdot 7}{4 \cdot 3}$

Step 10.3.3.1.2.2

Cancel the common factor.

$y = \frac{4 \cdot 7}{4 \cdot 3}$

Step 10.3.3.1.2.3

Rewrite the expression.

$y = \frac{7}{3}$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & \frac{11}{3} \\ - 1 & \frac{10}{3} \\ 0 & 3 \\ 1 & \frac{8}{3} \\ 2 & \frac{7}{3} \end{array}$

Step 12