Pre-Algebra Examples

$- 16 (x + 4) = 15 y$

Step 1

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

$- 16 ((- 2) + 4) = 15 y$

Step 2

Solve the equation for $y$ .

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Step 2.1

Rewrite the equation as $15 y = - 16 ((- 2) + 4)$ .

$15 y = - 16 ((- 2) + 4)$

Step 2.2

Simplify.

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Step 2.2.1

Add $- 2$ and $4$ .

$15 y = - 16 \cdot 2$

Step 2.2.2

Multiply $- 16$ by $2$ .

$15 y = - 32$

Step 2.3

Divide each term in $15 y = - 32$ by $15$ and simplify.

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Step 2.3.1

Divide each term in $15 y = - 32$ by $15$ .

$\frac{15 y}{15} = \frac{- 32}{15}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $15$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{15 y}{15} = \frac{- 32}{15}$

Step 2.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 32}{15}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Move the negative in front of the fraction.

$y = - \frac{32}{15}$

Step 3

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

$- 16 ((- 1) + 4) = 15 y$

Step 4

Solve the equation for $y$ .

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Step 4.1

Rewrite the equation as $15 y = - 16 ((- 1) + 4)$ .

$15 y = - 16 ((- 1) + 4)$

Step 4.2

Simplify.

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Step 4.2.1

Add $- 1$ and $4$ .

$15 y = - 16 \cdot 3$

Step 4.2.2

Multiply $- 16$ by $3$ .

$15 y = - 48$

Step 4.3

Divide each term in $15 y = - 48$ by $15$ and simplify.

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Step 4.3.1

Divide each term in $15 y = - 48$ by $15$ .

$\frac{15 y}{15} = \frac{- 48}{15}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $15$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{15 y}{15} = \frac{- 48}{15}$

Step 4.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 48}{15}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Cancel the common factor of $- 48$ and $15$ .

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Step 4.3.3.1.1

Factor $3$ out of $- 48$ .

$y = \frac{3 (- 16)}{15}$

Step 4.3.3.1.2

Cancel the common factors.

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Step 4.3.3.1.2.1

Factor $3$ out of $15$ .

$y = \frac{3 \cdot - 16}{3 \cdot 5}$

Step 4.3.3.1.2.2

Cancel the common factor.

$y = \frac{3 \cdot - 16}{3 \cdot 5}$

Step 4.3.3.1.2.3

Rewrite the expression.

$y = \frac{- 16}{5}$

Step 4.3.3.2

Move the negative in front of the fraction.

$y = - \frac{16}{5}$

Step 5

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

$- 16 ((0) + 4) = 15 y$

Step 6

Solve the equation for $y$ .

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Step 6.1

Rewrite the equation as $15 y = - 16 ((0) + 4)$ .

$15 y = - 16 ((0) + 4)$

Step 6.2

Simplify.

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Step 6.2.1

Add $0$ and $4$ .

$15 y = - 16 \cdot 4$

Step 6.2.2

Multiply $- 16$ by $4$ .

$15 y = - 64$

Step 6.3

Divide each term in $15 y = - 64$ by $15$ and simplify.

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Step 6.3.1

Divide each term in $15 y = - 64$ by $15$ .

$\frac{15 y}{15} = \frac{- 64}{15}$

Step 6.3.2

Simplify the left side.

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Step 6.3.2.1

Cancel the common factor of $15$ .

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Step 6.3.2.1.1

Cancel the common factor.

$\frac{15 y}{15} = \frac{- 64}{15}$

Step 6.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 64}{15}$

Step 6.3.3

Simplify the right side.

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Step 6.3.3.1

Move the negative in front of the fraction.

$y = - \frac{64}{15}$

Step 7

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

$- 16 ((1) + 4) = 15 y$

Step 8

Solve the equation for $y$ .

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Step 8.1

Rewrite the equation as $15 y = - 16 ((1) + 4)$ .

$15 y = - 16 ((1) + 4)$

Step 8.2

Simplify.

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Step 8.2.1

Add $1$ and $4$ .

$15 y = - 16 \cdot 5$

Step 8.2.2

Multiply $- 16$ by $5$ .

$15 y = - 80$

Step 8.3

Divide each term in $15 y = - 80$ by $15$ and simplify.

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Step 8.3.1

Divide each term in $15 y = - 80$ by $15$ .

$\frac{15 y}{15} = \frac{- 80}{15}$

Step 8.3.2

Simplify the left side.

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Step 8.3.2.1

Cancel the common factor of $15$ .

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Step 8.3.2.1.1

Cancel the common factor.

$\frac{15 y}{15} = \frac{- 80}{15}$

Step 8.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 80}{15}$

Step 8.3.3

Simplify the right side.

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Step 8.3.3.1

Cancel the common factor of $- 80$ and $15$ .

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Step 8.3.3.1.1

Factor $5$ out of $- 80$ .

$y = \frac{5 (- 16)}{15}$

Step 8.3.3.1.2

Cancel the common factors.

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Step 8.3.3.1.2.1

Factor $5$ out of $15$ .

$y = \frac{5 \cdot - 16}{5 \cdot 3}$

Step 8.3.3.1.2.2

Cancel the common factor.

$y = \frac{5 \cdot - 16}{5 \cdot 3}$

Step 8.3.3.1.2.3

Rewrite the expression.

$y = \frac{- 16}{3}$

Step 8.3.3.2

Move the negative in front of the fraction.

$y = - \frac{16}{3}$

Step 9

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

$- 16 ((2) + 4) = 15 y$

Step 10

Solve the equation for $y$ .

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Step 10.1

Rewrite the equation as $15 y = - 16 ((2) + 4)$ .

$15 y = - 16 ((2) + 4)$

Step 10.2

Simplify.

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Step 10.2.1

Add $2$ and $4$ .

$15 y = - 16 \cdot 6$

Step 10.2.2

Multiply $- 16$ by $6$ .

$15 y = - 96$

Step 10.3

Divide each term in $15 y = - 96$ by $15$ and simplify.

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Step 10.3.1

Divide each term in $15 y = - 96$ by $15$ .

$\frac{15 y}{15} = \frac{- 96}{15}$

Step 10.3.2

Simplify the left side.

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Step 10.3.2.1

Cancel the common factor of $15$ .

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Step 10.3.2.1.1

Cancel the common factor.

$\frac{15 y}{15} = \frac{- 96}{15}$

Step 10.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 96}{15}$

Step 10.3.3

Simplify the right side.

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Step 10.3.3.1

Cancel the common factor of $- 96$ and $15$ .

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Step 10.3.3.1.1

Factor $3$ out of $- 96$ .

$y = \frac{3 (- 32)}{15}$

Step 10.3.3.1.2

Cancel the common factors.

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Step 10.3.3.1.2.1

Factor $3$ out of $15$ .

$y = \frac{3 \cdot - 32}{3 \cdot 5}$

Step 10.3.3.1.2.2

Cancel the common factor.

$y = \frac{3 \cdot - 32}{3 \cdot 5}$

Step 10.3.3.1.2.3

Rewrite the expression.

$y = \frac{- 32}{5}$

Step 10.3.3.2

Move the negative in front of the fraction.

$y = - \frac{32}{5}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - \frac{32}{15} \\ - 1 & - \frac{16}{5} \\ 0 & - \frac{64}{15} \\ 1 & - \frac{16}{3} \\ 2 & - \frac{32}{5} \end{array}$

Step 12