Pre-Algebra Examples

$\frac{1}{2} \cdot (y + 5) + 3 = \frac{1}{4} \cdot (7 y - 11) - 8$

Step 1

Simplify $\frac{1}{2} \cdot (y + 5) + 3$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$\frac{1}{2} y + \frac{1}{2} \cdot 5 + 3 = \frac{1}{4} \cdot (7 y - 11) - 8$

Step 1.1.2

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

$\frac{y}{2} + \frac{1}{2} \cdot 5 + 3 = \frac{1}{4} \cdot (7 y - 11) - 8$

Step 1.1.3

Combine $\frac{1}{2}$ and $5$ .

$\frac{y}{2} + \frac{5}{2} + 3 = \frac{1}{4} \cdot (7 y - 11) - 8$

Step 1.2

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

$\frac{y}{2} + \frac{5}{2} + 3 \cdot \frac{2}{2} = \frac{1}{4} \cdot (7 y - 11) - 8$

Step 1.3

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

$\frac{y}{2} + \frac{5}{2} + \frac{3 \cdot 2}{2} = \frac{1}{4} \cdot (7 y - 11) - 8$

Step 1.4

Combine the numerators over the common denominator.

$\frac{y}{2} + \frac{5 + 3 \cdot 2}{2} = \frac{1}{4} \cdot (7 y - 11) - 8$

Step 1.5

Simplify the numerator.

Tap for more steps...

Step 1.5.1

Multiply $3$ by $2$ .

$\frac{y}{2} + \frac{5 + 6}{2} = \frac{1}{4} \cdot (7 y - 11) - 8$

Step 1.5.2

Add $5$ and $6$ .

$\frac{y}{2} + \frac{11}{2} = \frac{1}{4} \cdot (7 y - 11) - 8$

Step 2

Simplify $\frac{1}{4} \cdot (7 y - 11) - 8$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Apply the distributive property.

$\frac{y}{2} + \frac{11}{2} = \frac{1}{4} (7 y) + \frac{1}{4} \cdot - 11 - 8$

Step 2.1.2

Multiply $\frac{1}{4} (7 y)$ .

Tap for more steps...

Step 2.1.2.1

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

$\frac{y}{2} + \frac{11}{2} = \frac{7}{4} y + \frac{1}{4} \cdot - 11 - 8$

Step 2.1.2.2

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

$\frac{y}{2} + \frac{11}{2} = \frac{7 y}{4} + \frac{1}{4} \cdot - 11 - 8$

Step 2.1.3

Combine $\frac{1}{4}$ and $- 11$ .

$\frac{y}{2} + \frac{11}{2} = \frac{7 y}{4} + \frac{- 11}{4} - 8$

Step 2.1.4

Move the negative in front of the fraction.

$\frac{y}{2} + \frac{11}{2} = \frac{7 y}{4} - \frac{11}{4} - 8$

Step 2.2

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{y}{2} + \frac{11}{2} = \frac{7 y}{4} - \frac{11}{4} - 8 \cdot \frac{4}{4}$

Step 2.3

Combine $- 8$ and $\frac{4}{4}$ .

$\frac{y}{2} + \frac{11}{2} = \frac{7 y}{4} - \frac{11}{4} + \frac{- 8 \cdot 4}{4}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{y}{2} + \frac{11}{2} = \frac{7 y}{4} + \frac{- 11 - 8 \cdot 4}{4}$

Step 2.5

Simplify the numerator.

Tap for more steps...

Step 2.5.1

Multiply $- 8$ by $4$ .

$\frac{y}{2} + \frac{11}{2} = \frac{7 y}{4} + \frac{- 11 - 32}{4}$

Step 2.5.2

Subtract $32$ from $- 11$ .

$\frac{y}{2} + \frac{11}{2} = \frac{7 y}{4} + \frac{- 43}{4}$

Step 2.6

Move the negative in front of the fraction.

$\frac{y}{2} + \frac{11}{2} = \frac{7 y}{4} - \frac{43}{4}$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $\frac{7 y}{4}$ from both sides of the equation.

$\frac{y}{2} + \frac{11}{2} - \frac{7 y}{4} = - \frac{43}{4}$

Step 3.2

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

$\frac{y}{2} \cdot \frac{2}{2} - \frac{7 y}{4} + \frac{11}{2} = - \frac{43}{4}$

Step 3.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.3.1

Multiply $\frac{y}{2}$ by $\frac{2}{2}$ .

$\frac{y \cdot 2}{2 \cdot 2} - \frac{7 y}{4} + \frac{11}{2} = - \frac{43}{4}$

Step 3.3.2

Multiply $2$ by $2$ .

$\frac{y \cdot 2}{4} - \frac{7 y}{4} + \frac{11}{2} = - \frac{43}{4}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{y \cdot 2 - 7 y}{4} + \frac{11}{2} = - \frac{43}{4}$

Step 3.5

Subtract $7 y$ from $y \cdot 2$ .

Tap for more steps...

Step 3.5.1

Reorder $y$ and $2$ .

$\frac{2 \cdot y - 7 y}{4} + \frac{11}{2} = - \frac{43}{4}$

Step 3.5.2

Subtract $7 y$ from $2 \cdot y$ .

$\frac{- 5 \cdot y}{4} + \frac{11}{2} = - \frac{43}{4}$

Step 3.6

Move the negative in front of the fraction.

$- \frac{5 y}{4} + \frac{11}{2} = - \frac{43}{4}$

Step 4

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

Tap for more steps...

Step 4.1

Subtract $\frac{11}{2}$ from both sides of the equation.

$- \frac{5 y}{4} = - \frac{43}{4} - \frac{11}{2}$

Step 4.2

To write $- \frac{11}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{5 y}{4} = - \frac{43}{4} - \frac{11}{2} \cdot \frac{2}{2}$

Step 4.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.3.1

Multiply $\frac{11}{2}$ by $\frac{2}{2}$ .

$- \frac{5 y}{4} = - \frac{43}{4} - \frac{11 \cdot 2}{2 \cdot 2}$

Step 4.3.2

Multiply $2$ by $2$ .

$- \frac{5 y}{4} = - \frac{43}{4} - \frac{11 \cdot 2}{4}$

Step 4.4

Combine the numerators over the common denominator.

$- \frac{5 y}{4} = \frac{- 43 - 11 \cdot 2}{4}$

Step 4.5

Simplify the numerator.

Tap for more steps...

Step 4.5.1

Multiply $- 11$ by $2$ .

$- \frac{5 y}{4} = \frac{- 43 - 22}{4}$

Step 4.5.2

Subtract $22$ from $- 43$ .

$- \frac{5 y}{4} = \frac{- 65}{4}$

Step 4.6

Move the negative in front of the fraction.

$- \frac{5 y}{4} = - \frac{65}{4}$

Step 5

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 5 y = - 65$

Step 6

Divide each term in $- 5 y = - 65$ by $- 5$ and simplify.

Tap for more steps...

Step 6.1

Divide each term in $- 5 y = - 65$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{- 65}{- 5}$

Step 6.2

Simplify the left side.

Tap for more steps...

Step 6.2.1

Cancel the common factor of $- 5$ .

Tap for more steps...

Step 6.2.1.1

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{- 65}{- 5}$

Step 6.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 65}{- 5}$

Step 6.3

Simplify the right side.

Tap for more steps...

Step 6.3.1

Divide $- 65$ by $- 5$ .

$y = 13$