Precalculus Examples

$\frac{3 - 4 y}{6} - \frac{2 y - 3}{8} = 2 - y$

Step 1

Simplify $\frac{3 - 4 y}{6} - \frac{2 y - 3}{8}$ .

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Step 1.1

To write $\frac{3 - 4 y}{6}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 - 4 y}{6} \cdot \frac{4}{4} - \frac{2 y - 3}{8} = 2 - y$

Step 1.2

To write $- \frac{2 y - 3}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 - 4 y}{6} \cdot \frac{4}{4} - \frac{2 y - 3}{8} \cdot \frac{3}{3} = 2 - y$

Step 1.3

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{3 - 4 y}{6}$ by $\frac{4}{4}$ .

$\frac{(3 - 4 y) \cdot 4}{6 \cdot 4} - \frac{2 y - 3}{8} \cdot \frac{3}{3} = 2 - y$

Step 1.3.2

Multiply $6$ by $4$ .

$\frac{(3 - 4 y) \cdot 4}{24} - \frac{2 y - 3}{8} \cdot \frac{3}{3} = 2 - y$

Step 1.3.3

Multiply $\frac{2 y - 3}{8}$ by $\frac{3}{3}$ .

$\frac{(3 - 4 y) \cdot 4}{24} - \frac{(2 y - 3) \cdot 3}{8 \cdot 3} = 2 - y$

Step 1.3.4

Multiply $8$ by $3$ .

$\frac{(3 - 4 y) \cdot 4}{24} - \frac{(2 y - 3) \cdot 3}{24} = 2 - y$

Step 1.4

Combine the numerators over the common denominator.

$\frac{(3 - 4 y) \cdot 4 - (2 y - 3) \cdot 3}{24} = 2 - y$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Apply the distributive property.

$\frac{3 \cdot 4 - 4 y \cdot 4 - (2 y - 3) \cdot 3}{24} = 2 - y$

Step 1.5.2

Multiply $3$ by $4$ .

$\frac{12 - 4 y \cdot 4 - (2 y - 3) \cdot 3}{24} = 2 - y$

Step 1.5.3

Multiply $4$ by $- 4$ .

$\frac{12 - 16 y - (2 y - 3) \cdot 3}{24} = 2 - y$

Step 1.5.4

Apply the distributive property.

$\frac{12 - 16 y + (- (2 y) - - 3) \cdot 3}{24} = 2 - y$

Step 1.5.5

Multiply $2$ by $- 1$ .

$\frac{12 - 16 y + (- 2 y - - 3) \cdot 3}{24} = 2 - y$

Step 1.5.6

Multiply $- 1$ by $- 3$ .

$\frac{12 - 16 y + (- 2 y + 3) \cdot 3}{24} = 2 - y$

Step 1.5.7

Apply the distributive property.

$\frac{12 - 16 y - 2 y \cdot 3 + 3 \cdot 3}{24} = 2 - y$

Step 1.5.8

Multiply $3$ by $- 2$ .

$\frac{12 - 16 y - 6 y + 3 \cdot 3}{24} = 2 - y$

Step 1.5.9

Multiply $3$ by $3$ .

$\frac{12 - 16 y - 6 y + 9}{24} = 2 - y$

Step 1.5.10

Add $12$ and $9$ .

$\frac{- 16 y - 6 y + 21}{24} = 2 - y$

Step 1.5.11

Subtract $6 y$ from $- 16 y$ .

$\frac{- 22 y + 21}{24} = 2 - y$

Step 1.6

Simplify with factoring out.

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Step 1.6.1

Factor $- 1$ out of $- 22 y$ .

$\frac{- (22 y) + 21}{24} = 2 - y$

Step 1.6.2

Rewrite $21$ as $- 1 (- 21)$ .

$\frac{- (22 y) - 1 (- 21)}{24} = 2 - y$

Step 1.6.3

Factor $- 1$ out of $- (22 y) - 1 (- 21)$ .

$\frac{- (22 y - 21)}{24} = 2 - y$

Step 1.6.4

Simplify the expression.

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Step 1.6.4.1

Rewrite $- (22 y - 21)$ as $- 1 (22 y - 21)$ .

$\frac{- 1 (22 y - 21)}{24} = 2 - y$

Step 1.6.4.2

Move the negative in front of the fraction.

$- \frac{22 y - 21}{24} = 2 - y$

Step 2

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

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Step 2.1

Add $y$ to both sides of the equation.

$- \frac{22 y - 21}{24} + y = 2$

Step 2.2

To write $y$ as a fraction with a common denominator, multiply by $\frac{24}{24}$ .

$- \frac{22 y - 21}{24} + y \cdot \frac{24}{24} = 2$

Step 2.3

Combine $y$ and $\frac{24}{24}$ .

$- \frac{22 y - 21}{24} + \frac{y \cdot 24}{24} = 2$

Step 2.4

Combine the numerators over the common denominator.

$\frac{- (22 y - 21) + y \cdot 24}{24} = 2$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Apply the distributive property.

$\frac{- (22 y) - - 21 + y \cdot 24}{24} = 2$

Step 2.5.2

Multiply $22$ by $- 1$ .

$\frac{- 22 y - - 21 + y \cdot 24}{24} = 2$

Step 2.5.3

Multiply $- 1$ by $- 21$ .

$\frac{- 22 y + 21 + y \cdot 24}{24} = 2$

Step 2.5.4

Move $24$ to the left of $y$ .

$\frac{- 22 y + 21 + 24 \cdot y}{24} = 2$

Step 2.5.5

Add $- 22 y$ and $24 y$ .

$\frac{2 y + 21}{24} = 2$

Step 3

Multiply both sides by $24$ .

$\frac{2 y + 21}{24} \cdot 24 = 2 \cdot 24$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $24$ .

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Step 4.1.1.1

Cancel the common factor.

$\frac{2 y + 21}{24} \cdot 24 = 2 \cdot 24$

Step 4.1.1.2

Rewrite the expression.

$2 y + 21 = 2 \cdot 24$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $2$ by $24$ .

$2 y + 21 = 48$

Step 5

Solve for $y$ .

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Step 5.1

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

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Step 5.1.1

Subtract $21$ from both sides of the equation.

$2 y = 48 - 21$

Step 5.1.2

Subtract $21$ from $48$ .

$2 y = 27$

Step 5.2

Divide each term in $2 y = 27$ by $2$ and simplify.

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Step 5.2.1

Divide each term in $2 y = 27$ by $2$ .

$\frac{2 y}{2} = \frac{27}{2}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $2$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{27}{2}$

Step 5.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{27}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{27}{2}$

Decimal Form:

$y = 13.5$

Mixed Number Form:

$y = 13 \frac{1}{2}$