Algebra Examples

$y + 268 = \frac{1}{12} (x + 20)$

Step 1

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

$y + 268 = \frac{1}{12} \cdot ((- 2) + 20)$

Step 2

Solve the equation for $y$ .

Tap for more steps...

Step 2.1

Simplify $\frac{1}{12} \cdot ((- 2) + 20)$ .

Tap for more steps...

Step 2.1.1

Rewrite.

$y + 268 = 0 + 0 + \frac{1}{12} \cdot ((- 2) + 20)$

Step 2.1.2

Add $- 2$ and $20$ .

$y + 268 = \frac{1}{12} \cdot 18$

Step 2.1.3

Cancel the common factor of $6$ .

Tap for more steps...

Step 2.1.3.1

Factor $6$ out of $12$ .

$y + 268 = \frac{1}{6 (2)} \cdot 18$

Step 2.1.3.2

Factor $6$ out of $18$ .

$y + 268 = \frac{1}{6 \cdot 2} \cdot (6 \cdot 3)$

Step 2.1.3.3

Cancel the common factor.

$y + 268 = \frac{1}{6 \cdot 2} \cdot (6 \cdot 3)$

Step 2.1.3.4

Rewrite the expression.

$y + 268 = \frac{1}{2} \cdot 3$

Step 2.1.4

Combine $\frac{1}{2}$ and $3$ .

$y + 268 = \frac{3}{2}$

Step 2.2

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

Tap for more steps...

Step 2.2.1

Subtract $268$ from both sides of the equation.

$y = \frac{3}{2} - 268$

Step 2.2.2

To write $- 268$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{3}{2} - 268 \cdot \frac{2}{2}$

Step 2.2.3

Combine $- 268$ and $\frac{2}{2}$ .

$y = \frac{3}{2} + \frac{- 268 \cdot 2}{2}$

Step 2.2.4

Combine the numerators over the common denominator.

$y = \frac{3 - 268 \cdot 2}{2}$

Step 2.2.5

Simplify the numerator.

Tap for more steps...

Step 2.2.5.1

Multiply $- 268$ by $2$ .

$y = \frac{3 - 536}{2}$

Step 2.2.5.2

Subtract $536$ from $3$ .

$y = \frac{- 533}{2}$

Step 2.2.6

Move the negative in front of the fraction.

$y = - \frac{533}{2}$

Step 3

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

$y + 268 = \frac{1}{12} \cdot ((- 1) + 20)$

Step 4

Solve the equation for $y$ .

Tap for more steps...

Step 4.1

Simplify $\frac{1}{12} \cdot ((- 1) + 20)$ .

Tap for more steps...

Step 4.1.1

Rewrite.

$y + 268 = 0 + 0 + \frac{1}{12} \cdot ((- 1) + 20)$

Step 4.1.2

Add $- 1$ and $20$ .

$y + 268 = \frac{1}{12} \cdot 19$

Step 4.1.3

Combine $\frac{1}{12}$ and $19$ .

$y + 268 = \frac{19}{12}$

Step 4.2

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

Tap for more steps...

Step 4.2.1

Subtract $268$ from both sides of the equation.

$y = \frac{19}{12} - 268$

Step 4.2.2

To write $- 268$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$y = \frac{19}{12} - 268 \cdot \frac{12}{12}$

Step 4.2.3

Combine $- 268$ and $\frac{12}{12}$ .

$y = \frac{19}{12} + \frac{- 268 \cdot 12}{12}$

Step 4.2.4

Combine the numerators over the common denominator.

$y = \frac{19 - 268 \cdot 12}{12}$

Step 4.2.5

Simplify the numerator.

Tap for more steps...

Step 4.2.5.1

Multiply $- 268$ by $12$ .

$y = \frac{19 - 3216}{12}$

Step 4.2.5.2

Subtract $3216$ from $19$ .

$y = \frac{- 3197}{12}$

Step 4.2.6

Move the negative in front of the fraction.

$y = - \frac{3197}{12}$

Step 5

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

$y + 268 = \frac{1}{12} \cdot ((0) + 20)$

Step 6

Solve the equation for $y$ .

Tap for more steps...

Step 6.1

Simplify $\frac{1}{12} \cdot ((0) + 20)$ .

Tap for more steps...

Step 6.1.1

Add $0$ and $20$ .

$y + 268 = \frac{1}{12} \cdot 20$

Step 6.1.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 6.1.2.1

Factor $4$ out of $12$ .

$y + 268 = \frac{1}{4 (3)} \cdot 20$

Step 6.1.2.2

Factor $4$ out of $20$ .

$y + 268 = \frac{1}{4 \cdot 3} \cdot (4 \cdot 5)$

Step 6.1.2.3

Cancel the common factor.

$y + 268 = \frac{1}{4 \cdot 3} \cdot (4 \cdot 5)$

Step 6.1.2.4

Rewrite the expression.

$y + 268 = \frac{1}{3} \cdot 5$

Step 6.1.3

Combine $\frac{1}{3}$ and $5$ .

$y + 268 = \frac{5}{3}$

Step 6.2

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

Tap for more steps...

Step 6.2.1

Subtract $268$ from both sides of the equation.

$y = \frac{5}{3} - 268$

Step 6.2.2

To write $- 268$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = \frac{5}{3} - 268 \cdot \frac{3}{3}$

Step 6.2.3

Combine $- 268$ and $\frac{3}{3}$ .

$y = \frac{5}{3} + \frac{- 268 \cdot 3}{3}$

Step 6.2.4

Combine the numerators over the common denominator.

$y = \frac{5 - 268 \cdot 3}{3}$

Step 6.2.5

Simplify the numerator.

Tap for more steps...

Step 6.2.5.1

Multiply $- 268$ by $3$ .

$y = \frac{5 - 804}{3}$

Step 6.2.5.2

Subtract $804$ from $5$ .

$y = \frac{- 799}{3}$

Step 6.2.6

Move the negative in front of the fraction.

$y = - \frac{799}{3}$

Step 7

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

$y + 268 = \frac{1}{12} \cdot ((1) + 20)$

Step 8

Solve the equation for $y$ .

Tap for more steps...

Step 8.1

Simplify $\frac{1}{12} \cdot ((1) + 20)$ .

Tap for more steps...

Step 8.1.1

Rewrite.

$y + 268 = 0 + 0 + \frac{1}{12} \cdot ((1) + 20)$

Step 8.1.2

Add $1$ and $20$ .

$y + 268 = \frac{1}{12} \cdot 21$

Step 8.1.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 8.1.3.1

Factor $3$ out of $12$ .

$y + 268 = \frac{1}{3 (4)} \cdot 21$

Step 8.1.3.2

Factor $3$ out of $21$ .

$y + 268 = \frac{1}{3 \cdot 4} \cdot (3 \cdot 7)$

Step 8.1.3.3

Cancel the common factor.

$y + 268 = \frac{1}{3 \cdot 4} \cdot (3 \cdot 7)$

Step 8.1.3.4

Rewrite the expression.

$y + 268 = \frac{1}{4} \cdot 7$

Step 8.1.4

Combine $\frac{1}{4}$ and $7$ .

$y + 268 = \frac{7}{4}$

Step 8.2

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

Tap for more steps...

Step 8.2.1

Subtract $268$ from both sides of the equation.

$y = \frac{7}{4} - 268$

Step 8.2.2

To write $- 268$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = \frac{7}{4} - 268 \cdot \frac{4}{4}$

Step 8.2.3

Combine $- 268$ and $\frac{4}{4}$ .

$y = \frac{7}{4} + \frac{- 268 \cdot 4}{4}$

Step 8.2.4

Combine the numerators over the common denominator.

$y = \frac{7 - 268 \cdot 4}{4}$

Step 8.2.5

Simplify the numerator.

Tap for more steps...

Step 8.2.5.1

Multiply $- 268$ by $4$ .

$y = \frac{7 - 1072}{4}$

Step 8.2.5.2

Subtract $1072$ from $7$ .

$y = \frac{- 1065}{4}$

Step 8.2.6

Move the negative in front of the fraction.

$y = - \frac{1065}{4}$

Step 9

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

$y + 268 = \frac{1}{12} \cdot ((2) + 20)$

Step 10

Solve the equation for $y$ .

Tap for more steps...

Step 10.1

Simplify $\frac{1}{12} \cdot ((2) + 20)$ .

Tap for more steps...

Step 10.1.1

Rewrite.

$y + 268 = 0 + 0 + \frac{1}{12} \cdot ((2) + 20)$

Step 10.1.2

Add $2$ and $20$ .

$y + 268 = \frac{1}{12} \cdot 22$

Step 10.1.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 10.1.3.1

Factor $2$ out of $12$ .

$y + 268 = \frac{1}{2 (6)} \cdot 22$

Step 10.1.3.2

Factor $2$ out of $22$ .

$y + 268 = \frac{1}{2 \cdot 6} \cdot (2 \cdot 11)$

Step 10.1.3.3

Cancel the common factor.

$y + 268 = \frac{1}{2 \cdot 6} \cdot (2 \cdot 11)$

Step 10.1.3.4

Rewrite the expression.

$y + 268 = \frac{1}{6} \cdot 11$

Step 10.1.4

Combine $\frac{1}{6}$ and $11$ .

$y + 268 = \frac{11}{6}$

Step 10.2

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

Tap for more steps...

Step 10.2.1

Subtract $268$ from both sides of the equation.

$y = \frac{11}{6} - 268$

Step 10.2.2

To write $- 268$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$y = \frac{11}{6} - 268 \cdot \frac{6}{6}$

Step 10.2.3

Combine $- 268$ and $\frac{6}{6}$ .

$y = \frac{11}{6} + \frac{- 268 \cdot 6}{6}$

Step 10.2.4

Combine the numerators over the common denominator.

$y = \frac{11 - 268 \cdot 6}{6}$

Step 10.2.5

Simplify the numerator.

Tap for more steps...

Step 10.2.5.1

Multiply $- 268$ by $6$ .

$y = \frac{11 - 1608}{6}$

Step 10.2.5.2

Subtract $1608$ from $11$ .

$y = \frac{- 1597}{6}$

Step 10.2.6

Move the negative in front of the fraction.

$y = - \frac{1597}{6}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - \frac{533}{2} \\ - 1 & - \frac{3197}{12} \\ 0 & - \frac{799}{3} \\ 1 & - \frac{1065}{4} \\ 2 & - \frac{1597}{6} \end{array}$

Step 12