Solve for y -3/2y+1/3y=5

$- \frac{3}{2} y + \frac{1}{3} y = 5$

Simplify $- \frac{3}{2} y + \frac{1}{3} y$ .

Tap for more steps…

Simplify each term.

Tap for more steps…

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

$- \frac{y \cdot 3}{2} + \frac{1}{3} y = 5$

Move $3$ to the left of $y$ .

$- \frac{3 \cdot y}{2} + \frac{1}{3} y = 5$

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

$- \frac{3 y}{2} + \frac{y}{3} = 5$

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

$- \frac{3 y}{2} \cdot \frac{3}{3} + \frac{y}{3} = 5$

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

$- \frac{3 y}{2} \cdot \frac{3}{3} + \frac{y}{3} \cdot \frac{2}{2} = 5$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps…

Multiply $\frac{3 y}{2}$ and $\frac{3}{3}$ .

$- \frac{3 y \cdot 3}{2 \cdot 3} + \frac{y}{3} \cdot \frac{2}{2} = 5$

Multiply $2$ by $3$ .

$- \frac{3 y \cdot 3}{6} + \frac{y}{3} \cdot \frac{2}{2} = 5$

Multiply $\frac{y}{3}$ and $\frac{2}{2}$ .

$- \frac{3 y \cdot 3}{6} + \frac{y \cdot 2}{3 \cdot 2} = 5$

Multiply $3$ by $2$ .

$- \frac{3 y \cdot 3}{6} + \frac{y \cdot 2}{6} = 5$

Combine the numerators over the common denominator.

$\frac{- 3 y \cdot 3 + y \cdot 2}{6} = 5$

Simplify the numerator.

Tap for more steps…

Factor $y$ out of $- 3 y \cdot 3 + y \cdot 2$ .

Tap for more steps…

Factor $y$ out of $- 3 y \cdot 3$ .

$\frac{y (- 3 \cdot 3) + y \cdot 2}{6} = 5$

Factor $y$ out of $y \cdot 2$ .

$\frac{y (- 3 \cdot 3) + y (2)}{6} = 5$

Factor $y$ out of $y (- 3 \cdot 3) + y (2)$ .

$\frac{y (- 3 \cdot 3 + 2)}{6} = 5$

Multiply $- 3$ by $3$ .

$\frac{y (- 9 + 2)}{6} = 5$

Add $- 9$ and $2$ .

$\frac{y \cdot - 7}{6} = 5$

Simplify the expression.

Tap for more steps…

Move $- 7$ to the left of $y$ .

$\frac{- 7 \cdot y}{6} = 5$

Move the negative in front of the fraction.

$- \frac{7 y}{6} = 5$

Multiply both sides of the equation by $- \frac{6}{7}$ .

$- \frac{6}{7} \cdot (- \frac{7 y}{6}) = - \frac{6}{7} \cdot 5$

Simplify both sides of the equation.

Tap for more steps…

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

Tap for more steps…

Cancel the common factor of $6$ .

Tap for more steps…

Move the leading negative in $- \frac{6}{7}$ into the numerator.

$\frac{- 6}{7} \cdot (- \frac{7 y}{6}) = - \frac{6}{7} \cdot 5$

Move the leading negative in $- \frac{7 y}{6}$ into the numerator.

$\frac{- 6}{7} \cdot \frac{- 7 y}{6} = - \frac{6}{7} \cdot 5$

Factor $6$ out of $- 6$ .

$\frac{6 (- 1)}{7} \cdot \frac{- 7 y}{6} = - \frac{6}{7} \cdot 5$

Cancel the common factor.

$\frac{6 \cdot - 1}{7} \cdot \frac{- 7 y}{6} = - \frac{6}{7} \cdot 5$

Rewrite the expression.

$\frac{- 1}{7} \cdot (- 7 y) = - \frac{6}{7} \cdot 5$

Cancel the common factor of $7$ .

Tap for more steps…

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

$\frac{- 1}{7} \cdot (7 (- y)) = - \frac{6}{7} \cdot 5$

Cancel the common factor.

$\frac{- 1}{7} \cdot (7 (- y)) = - \frac{6}{7} \cdot 5$

Rewrite the expression.

$- 1 \cdot (- y) = - \frac{6}{7} \cdot 5$

Multiply.

Tap for more steps…

Multiply $- 1$ by $- 1$ .

$1 \cdot y = - \frac{6}{7} \cdot 5$

Multiply $y$ by $1$ .

$y = - \frac{6}{7} \cdot 5$

Simplify $- \frac{6}{7} \cdot 5$ .

Tap for more steps…

Multiply $- \frac{6}{7} \cdot 5$ .

Tap for more steps…

Multiply $5$ by $- 1$ .

$y = - 5 (\frac{6}{7})$

Combine $- 5$ and $\frac{6}{7}$ .

$y = \frac{- 5 \cdot 6}{7}$

Multiply $- 5$ by $6$ .

$y = \frac{- 30}{7}$

Move the negative in front of the fraction.

$y = - \frac{30}{7}$

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{30}{7}$

Decimal Form:

$y = - 4.\overline{285714}$

Mixed Number Form:

$y = - 4 \frac{2}{7}$

Solve for y -3/2y+1/3y=5

Meet the Team our Math Expers

Our Professionals

Robert Kristofer

Anna Frok

Magnus Flores

Lydia Fran

We are MathExperts

We can solve all your math problems