Solve for y 1/5(y+3)+3=1/10(7y-4)-5

$\frac{1}{5} \cdot (y + 3) + 3 = \frac{1}{10} \cdot (7 y - 4) - 5$

Step 1

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

Simplify each term.

Apply the distributive property.

$\frac{1}{5} y + \frac{1}{5} \cdot 3 + 3 = \frac{1}{10} \cdot (7 y - 4) - 5$

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

$\frac{y}{5} + \frac{1}{5} \cdot 3 + 3 = \frac{1}{10} \cdot (7 y - 4) - 5$

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

$\frac{y}{5} + \frac{3}{5} + 3 = \frac{1}{10} \cdot (7 y - 4) - 5$

To write $3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{y}{5} + \frac{3}{5} + 3 \cdot \frac{5}{5} = \frac{1}{10} \cdot (7 y - 4) - 5$

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

$\frac{y}{5} + \frac{3}{5} + \frac{3 \cdot 5}{5} = \frac{1}{10} \cdot (7 y - 4) - 5$

Combine the numerators over the common denominator.

$\frac{y}{5} + \frac{3 + 3 \cdot 5}{5} = \frac{1}{10} \cdot (7 y - 4) - 5$

Simplify the numerator.

Multiply $3$ by $5$ .

$\frac{y}{5} + \frac{3 + 15}{5} = \frac{1}{10} \cdot (7 y - 4) - 5$

Add $3$ and $15$ .

$\frac{y}{5} + \frac{18}{5} = \frac{1}{10} \cdot (7 y - 4) - 5$

Step 2

Simplify $\frac{1}{10} \cdot (7 y - 4) - 5$ .

Simplify each term.

Apply the distributive property.

$\frac{y}{5} + \frac{18}{5} = \frac{1}{10} (7 y) + \frac{1}{10} \cdot - 4 - 5$

Multiply $\frac{1}{10} (7 y)$ .

Combine $7$ and $\frac{1}{10}$ .

$\frac{y}{5} + \frac{18}{5} = \frac{7}{10} y + \frac{1}{10} \cdot - 4 - 5$

Combine $\frac{7}{10}$ and $y$ .

$\frac{y}{5} + \frac{18}{5} = \frac{7 y}{10} + \frac{1}{10} \cdot - 4 - 5$

Cancel the common factor of $2$ .

Factor $2$ out of $10$ .

$\frac{y}{5} + \frac{18}{5} = \frac{7 y}{10} + \frac{1}{2 (5)} \cdot - 4 - 5$

Factor $2$ out of $- 4$ .

$\frac{y}{5} + \frac{18}{5} = \frac{7 y}{10} + \frac{1}{2 \cdot 5} \cdot (2 \cdot - 2) - 5$

Cancel the common factor.

$\frac{y}{5} + \frac{18}{5} = \frac{7 y}{10} + \frac{1}{2 \cdot 5} \cdot (2 \cdot - 2) - 5$

Rewrite the expression.

$\frac{y}{5} + \frac{18}{5} = \frac{7 y}{10} + \frac{1}{5} \cdot - 2 - 5$

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

$\frac{y}{5} + \frac{18}{5} = \frac{7 y}{10} + \frac{- 2}{5} - 5$

Move the negative in front of the fraction.

$\frac{y}{5} + \frac{18}{5} = \frac{7 y}{10} - \frac{2}{5} - 5$

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{y}{5} + \frac{18}{5} = \frac{7 y}{10} - \frac{2}{5} - 5 \cdot \frac{5}{5}$

Combine $- 5$ and $\frac{5}{5}$ .

$\frac{y}{5} + \frac{18}{5} = \frac{7 y}{10} - \frac{2}{5} + \frac{- 5 \cdot 5}{5}$

Combine the numerators over the common denominator.

$\frac{y}{5} + \frac{18}{5} = \frac{7 y}{10} + \frac{- 2 - 5 \cdot 5}{5}$

Simplify the numerator.

Multiply $- 5$ by $5$ .

$\frac{y}{5} + \frac{18}{5} = \frac{7 y}{10} + \frac{- 2 - 25}{5}$

Subtract $25$ from $- 2$ .

$\frac{y}{5} + \frac{18}{5} = \frac{7 y}{10} + \frac{- 27}{5}$

Move the negative in front of the fraction.

$\frac{y}{5} + \frac{18}{5} = \frac{7 y}{10} - \frac{27}{5}$

Step 3

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

Subtract $\frac{7 y}{10}$ from both sides of the equation.

$\frac{y}{5} + \frac{18}{5} - \frac{7 y}{10} = - \frac{27}{5}$

To write $\frac{y}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{y}{5} \cdot \frac{2}{2} - \frac{7 y}{10} + \frac{18}{5} = - \frac{27}{5}$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{y}{5}$ by $\frac{2}{2}$ .

$\frac{y \cdot 2}{5 \cdot 2} - \frac{7 y}{10} + \frac{18}{5} = - \frac{27}{5}$

Multiply $5$ by $2$ .

$\frac{y \cdot 2}{10} - \frac{7 y}{10} + \frac{18}{5} = - \frac{27}{5}$

Combine the numerators over the common denominator.

$\frac{y \cdot 2 - 7 y}{10} + \frac{18}{5} = - \frac{27}{5}$

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

Reorder $y$ and $2$ .

$\frac{2 \cdot y - 7 y}{10} + \frac{18}{5} = - \frac{27}{5}$

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

$\frac{- 5 \cdot y}{10} + \frac{18}{5} = - \frac{27}{5}$

Simplify each term.

Cancel the common factor of $- 5$ and $10$ .

Factor $5$ out of $- 5 \cdot y$ .

$\frac{5 (- y)}{10} + \frac{18}{5} = - \frac{27}{5}$

Cancel the common factors.

Factor $5$ out of $10$ .

$\frac{5 (- y)}{5 (2)} + \frac{18}{5} = - \frac{27}{5}$

Cancel the common factor.

$\frac{5 (- y)}{5 \cdot 2} + \frac{18}{5} = - \frac{27}{5}$

Rewrite the expression.

$\frac{- y}{2} + \frac{18}{5} = - \frac{27}{5}$

Move the negative in front of the fraction.

$- \frac{y}{2} + \frac{18}{5} = - \frac{27}{5}$

Step 4

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

Subtract $\frac{18}{5}$ from both sides of the equation.

$- \frac{y}{2} = - \frac{27}{5} - \frac{18}{5}$

Combine the numerators over the common denominator.

$- \frac{y}{2} = \frac{- 27 - 18}{5}$

Subtract $18$ from $- 27$ .

$- \frac{y}{2} = \frac{- 45}{5}$

Divide $- 45$ by $5$ .

$- \frac{y}{2} = - 9$

Step 5

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{y}{2}) = - 2 \cdot - 9$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{y}{2})$ .

Cancel the common factor of $2$ .

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

$- 2 \frac{- y}{2} = - 2 \cdot - 9$

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- y}{2} = - 2 \cdot - 9$

Cancel the common factor.

$2 \cdot - 1 \frac{- y}{2} = - 2 \cdot - 9$

Rewrite the expression.

$- - y = - 2 \cdot - 9$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 y = - 2 \cdot - 9$

Multiply $y$ by $1$ .

$y = - 2 \cdot - 9$

Simplify the right side.

Multiply $- 2$ by $- 9$ .

$y = 18$

Solve for y 1/5*(y+3)+3=1/10*(7y-4)-5

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Solve for y 1/5(y+3)+3=1/10(7y-4)-5