Solve for j 3/4j+2/5=-2 3/10

$\frac{3}{4} j + \frac{2}{5} = - 2 \frac{3}{10}$

Simplify the left side.

Combine $\frac{3}{4}$ and $j$ .

$\frac{3 j}{4} + \frac{2}{5} = - 2 \frac{3}{10}$

Simplify the right side.

Convert $2 \frac{3}{10}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{3 j}{4} + \frac{2}{5} = - (2 + \frac{3}{10})$

Add $2$ and $\frac{3}{10}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{3 j}{4} + \frac{2}{5} = - (2 \cdot \frac{10}{10} + \frac{3}{10})$

Combine $2$ and $\frac{10}{10}$ .

$\frac{3 j}{4} + \frac{2}{5} = - (\frac{2 \cdot 10}{10} + \frac{3}{10})$

Combine the numerators over the common denominator.

$\frac{3 j}{4} + \frac{2}{5} = - \frac{2 \cdot 10 + 3}{10}$

Simplify the numerator.

Multiply $2$ by $10$ .

$\frac{3 j}{4} + \frac{2}{5} = - \frac{20 + 3}{10}$

Add $20$ and $3$ .

$\frac{3 j}{4} + \frac{2}{5} = - \frac{23}{10}$

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

Subtract $\frac{2}{5}$ from both sides of the equation.

$\frac{3 j}{4} = - \frac{23}{10} - \frac{2}{5}$

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

$\frac{3 j}{4} = - \frac{23}{10} - \frac{2}{5} \cdot \frac{2}{2}$

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

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

$\frac{3 j}{4} = - \frac{23}{10} - \frac{2 \cdot 2}{5 \cdot 2}$

Multiply $5$ by $2$ .

$\frac{3 j}{4} = - \frac{23}{10} - \frac{2 \cdot 2}{10}$

Combine the numerators over the common denominator.

$\frac{3 j}{4} = \frac{- 23 - 2 \cdot 2}{10}$

Simplify the numerator.

Multiply $- 2$ by $2$ .

$\frac{3 j}{4} = \frac{- 23 - 4}{10}$

Subtract $4$ from $- 23$ .

$\frac{3 j}{4} = \frac{- 27}{10}$

Move the negative in front of the fraction.

$\frac{3 j}{4} = - \frac{27}{10}$

Multiply both sides of the equation by $\frac{4}{3}$ .

$\frac{4}{3} \cdot \frac{3 j}{4} = \frac{4}{3} (- \frac{27}{10})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{3} \cdot \frac{3 j}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 j}{4} = \frac{4}{3} (- \frac{27}{10})$

Rewrite the expression.

$\frac{1}{3} (3 j) = \frac{4}{3} (- \frac{27}{10})$

Cancel the common factor of $3$ .

Factor $3$ out of $3 j$ .

$\frac{1}{3} (3 (j)) = \frac{4}{3} (- \frac{27}{10})$

Cancel the common factor.

$\frac{1}{3} (3 j) = \frac{4}{3} (- \frac{27}{10})$

Rewrite the expression.

$j = \frac{4}{3} (- \frac{27}{10})$

Simplify the right side.

Simplify $\frac{4}{3} (- \frac{27}{10})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{27}{10}$ into the numerator.

$j = \frac{4}{3} \cdot \frac{- 27}{10}$

Factor $2$ out of $4$ .

$j = \frac{2 (2)}{3} \cdot \frac{- 27}{10}$

Factor $2$ out of $10$ .

$j = \frac{2 \cdot 2}{3} \cdot \frac{- 27}{2 \cdot 5}$

Cancel the common factor.

$j = \frac{2 \cdot 2}{3} \cdot \frac{- 27}{2 \cdot 5}$

Rewrite the expression.

$j = \frac{2}{3} \cdot \frac{- 27}{5}$

Cancel the common factor of $3$ .

Factor $3$ out of $- 27$ .

$j = \frac{2}{3} \cdot \frac{3 (- 9)}{5}$

Cancel the common factor.

$j = \frac{2}{3} \cdot \frac{3 \cdot - 9}{5}$

Rewrite the expression.

$j = 2 (\frac{- 9}{5})$

Combine $2$ and $\frac{- 9}{5}$ .

$j = \frac{2 \cdot - 9}{5}$

Simplify the expression.

Multiply $2$ by $- 9$ .

$j = \frac{- 18}{5}$

Move the negative in front of the fraction.

$j = - \frac{18}{5}$

The result can be shown in multiple forms.

Exact Form:

$j = - \frac{18}{5}$

Decimal Form:

$j = - 3.6$

Mixed Number Form:

$j = - 3 \frac{3}{5}$

Solve for j 3/4j+2/5=-2 3/10

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