Basic Math Examples

$\frac{7 y - 8}{3} = 10 - \frac{7 y - 8}{6}$

Step 1

Multiply both sides by $3$ .

$\frac{7 y - 8}{3} \cdot 3 = (10 - \frac{7 y - 8}{6}) \cdot 3$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $3$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{7 y - 8}{3} \cdot 3 = (10 - \frac{7 y - 8}{6}) \cdot 3$

Step 2.1.1.2

Rewrite the expression.

$7 y - 8 = (10 - \frac{7 y - 8}{6}) \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(10 - \frac{7 y - 8}{6}) \cdot 3$ .

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Step 2.2.1.1

To write $10$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$7 y - 8 = (10 \cdot \frac{6}{6} - \frac{7 y - 8}{6}) \cdot 3$

Step 2.2.1.2

Simplify terms.

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Step 2.2.1.2.1

Combine $10$ and $\frac{6}{6}$ .

$7 y - 8 = (\frac{10 \cdot 6}{6} - \frac{7 y - 8}{6}) \cdot 3$

Step 2.2.1.2.2

Combine the numerators over the common denominator.

$7 y - 8 = \frac{10 \cdot 6 - (7 y - 8)}{6} \cdot 3$

Step 2.2.1.3

Simplify the numerator.

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Step 2.2.1.3.1

Multiply $10$ by $6$ .

$7 y - 8 = \frac{60 - (7 y - 8)}{6} \cdot 3$

Step 2.2.1.3.2

Apply the distributive property.

$7 y - 8 = \frac{60 - (7 y) - - 8}{6} \cdot 3$

Step 2.2.1.3.3

Multiply $7$ by $- 1$ .

$7 y - 8 = \frac{60 - 7 y - - 8}{6} \cdot 3$

Step 2.2.1.3.4

Multiply $- 1$ by $- 8$ .

$7 y - 8 = \frac{60 - 7 y + 8}{6} \cdot 3$

Step 2.2.1.3.5

Add $60$ and $8$ .

$7 y - 8 = \frac{- 7 y + 68}{6} \cdot 3$

Step 2.2.1.4

Simplify terms.

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Step 2.2.1.4.1

Cancel the common factor of $3$ .

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Step 2.2.1.4.1.1

Factor $3$ out of $6$ .

$7 y - 8 = \frac{- 7 y + 68}{3 (2)} \cdot 3$

Step 2.2.1.4.1.2

Cancel the common factor.

$7 y - 8 = \frac{- 7 y + 68}{3 \cdot 2} \cdot 3$

Step 2.2.1.4.1.3

Rewrite the expression.

$7 y - 8 = \frac{- 7 y + 68}{2}$

Step 2.2.1.4.2

Factor $- 1$ out of $- 7 y$ .

$7 y - 8 = \frac{- (7 y) + 68}{2}$

Step 2.2.1.4.3

Rewrite $68$ as $- 1 (- 68)$ .

$7 y - 8 = \frac{- (7 y) - 1 (- 68)}{2}$

Step 2.2.1.4.4

Factor $- 1$ out of $- (7 y) - 1 (- 68)$ .

$7 y - 8 = \frac{- (7 y - 68)}{2}$

Step 2.2.1.4.5

Simplify the expression.

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Step 2.2.1.4.5.1

Rewrite $- (7 y - 68)$ as $- 1 (7 y - 68)$ .

$7 y - 8 = \frac{- 1 (7 y - 68)}{2}$

Step 2.2.1.4.5.2

Move the negative in front of the fraction.

$7 y - 8 = - \frac{7 y - 68}{2}$

Step 3

Solve for $y$ .

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Step 3.1

Multiply both sides by $2$ .

$(7 y - 8) \cdot 2 = - \frac{7 y - 68}{2} \cdot 2$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Simplify $(7 y - 8) \cdot 2$ .

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Step 3.2.1.1.1

Apply the distributive property.

$7 y \cdot 2 - 8 \cdot 2 = - \frac{7 y - 68}{2} \cdot 2$

Step 3.2.1.1.2

Multiply.

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Step 3.2.1.1.2.1

Multiply $2$ by $7$ .

$14 y - 8 \cdot 2 = - \frac{7 y - 68}{2} \cdot 2$

Step 3.2.1.1.2.2

Multiply $- 8$ by $2$ .

$14 y - 16 = - \frac{7 y - 68}{2} \cdot 2$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $- \frac{7 y - 68}{2} \cdot 2$ .

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Step 3.2.2.1.1

Cancel the common factor of $2$ .

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Step 3.2.2.1.1.1

Move the leading negative in $- \frac{7 y - 68}{2}$ into the numerator.

$14 y - 16 = \frac{- (7 y - 68)}{2} \cdot 2$

Step 3.2.2.1.1.2

Cancel the common factor.

$14 y - 16 = \frac{- (7 y - 68)}{2} \cdot 2$

Step 3.2.2.1.1.3

Rewrite the expression.

$14 y - 16 = - (7 y - 68)$

Step 3.2.2.1.2

Apply the distributive property.

$14 y - 16 = - (7 y) - - 68$

Step 3.2.2.1.3

Multiply.

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Step 3.2.2.1.3.1

Multiply $7$ by $- 1$ .

$14 y - 16 = - 7 y - - 68$

Step 3.2.2.1.3.2

Multiply $- 1$ by $- 68$ .

$14 y - 16 = - 7 y + 68$

Step 3.3

Solve for $y$ .

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Step 3.3.1

Move all terms containing $y$ to the left side of the equation.

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Step 3.3.1.1

Add $7 y$ to both sides of the equation.

$14 y - 16 + 7 y = 68$

Step 3.3.1.2

Add $14 y$ and $7 y$ .

$21 y - 16 = 68$

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

Add $16$ to both sides of the equation.

$21 y = 68 + 16$

Step 3.3.2.2

Add $68$ and $16$ .

$21 y = 84$

Step 3.3.3

Divide each term in $21 y = 84$ by $21$ and simplify.

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Step 3.3.3.1

Divide each term in $21 y = 84$ by $21$ .

$\frac{21 y}{21} = \frac{84}{21}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $21$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{21 y}{21} = \frac{84}{21}$

Step 3.3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{84}{21}$

Step 3.3.3.3

Simplify the right side.

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Step 3.3.3.3.1

Divide $84$ by $21$ .

$y = 4$