Solve for j 3j-5=8+1/2j+1/3j

$3 j - 5 = 8 + \frac{1}{2} j + \frac{1}{3} j$

Since $j$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$8 + \frac{1}{2} j + \frac{1}{3} j = 3 j - 5$

Simplify $8 + \frac{1}{2} j + \frac{1}{3} j$ .

Simplify each term.

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

$8 + \frac{j}{2} + \frac{1}{3} j = 3 j - 5$

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

$8 + \frac{j}{2} + \frac{j}{3} = 3 j - 5$

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

$8 + \frac{j}{2} \cdot \frac{3}{3} + \frac{j}{3} = 3 j - 5$

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

$8 + \frac{j}{2} \cdot \frac{3}{3} + \frac{j}{3} \cdot \frac{2}{2} = 3 j - 5$

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

Multiply $\frac{j}{2}$ by $\frac{3}{3}$ .

$8 + \frac{j \cdot 3}{2 \cdot 3} + \frac{j}{3} \cdot \frac{2}{2} = 3 j - 5$

Multiply $2$ by $3$ .

$8 + \frac{j \cdot 3}{6} + \frac{j}{3} \cdot \frac{2}{2} = 3 j - 5$

Multiply $\frac{j}{3}$ by $\frac{2}{2}$ .

$8 + \frac{j \cdot 3}{6} + \frac{j \cdot 2}{3 \cdot 2} = 3 j - 5$

Multiply $3$ by $2$ .

$8 + \frac{j \cdot 3}{6} + \frac{j \cdot 2}{6} = 3 j - 5$

Combine the numerators over the common denominator.

$8 + \frac{j \cdot 3 + j \cdot 2}{6} = 3 j - 5$

Reorder $j$ and $2$ .

$8 + \frac{3 \cdot j + 2 \cdot j}{6} = 3 j - 5$

Add $3 \cdot j$ and $2 \cdot j$ .

$8 + \frac{5 j}{6} = 3 j - 5$

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

Subtract $3 j$ from both sides of the equation.

$8 + \frac{5 j}{6} - 3 j = - 5$

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

$8 + \frac{5 j}{6} - 3 j \cdot \frac{6}{6} = - 5$

Combine $- 3 j$ and $\frac{6}{6}$ .

$8 + \frac{5 j}{6} + \frac{- 3 j \cdot 6}{6} = - 5$

Combine the numerators over the common denominator.

$8 + \frac{5 j - 3 j \cdot 6}{6} = - 5$

Simplify each term.

Simplify the numerator.

Factor $j$ out of $5 j - 3 j \cdot 6$ .

Factor $j$ out of $5 j$ .

$8 + \frac{j \cdot 5 - 3 j \cdot 6}{6} = - 5$

Factor $j$ out of $- 3 j \cdot 6$ .

$8 + \frac{j \cdot 5 + j (- 3 \cdot 6)}{6} = - 5$

Factor $j$ out of $j \cdot 5 + j (- 3 \cdot 6)$ .

$8 + \frac{j (5 - 3 \cdot 6)}{6} = - 5$

Multiply $- 3$ by $6$ .

$8 + \frac{j (5 - 18)}{6} = - 5$

Subtract $18$ from $5$ .

$8 + \frac{j \cdot - 13}{6} = - 5$

Move $- 13$ to the left of $j$ .

$8 + \frac{- 13 \cdot j}{6} = - 5$

Move the negative in front of the fraction.

$8 - \frac{13 j}{6} = - 5$

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

Subtract $8$ from both sides of the equation.

$- \frac{13 j}{6} = - 5 - 8$

Subtract $8$ from $- 5$ .

$- \frac{13 j}{6} = - 13$

Multiply both sides of the equation by $- \frac{6}{13}$ .

$- \frac{6}{13} (- \frac{13 j}{6}) = - \frac{6}{13} \cdot - 13$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{6}{13} (- \frac{13 j}{6})$ .

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{6}{13}$ into the numerator.

$\frac{- 6}{13} (- \frac{13 j}{6}) = - \frac{6}{13} \cdot - 13$

Move the leading negative in $- \frac{13 j}{6}$ into the numerator.

$\frac{- 6}{13} \cdot \frac{- 13 j}{6} = - \frac{6}{13} \cdot - 13$

Factor $6$ out of $- 6$ .

$\frac{6 (- 1)}{13} \cdot \frac{- 13 j}{6} = - \frac{6}{13} \cdot - 13$

Cancel the common factor.

$\frac{6 \cdot - 1}{13} \cdot \frac{- 13 j}{6} = - \frac{6}{13} \cdot - 13$

Rewrite the expression.

$\frac{- 1}{13} (- 13 j) = - \frac{6}{13} \cdot - 13$

Cancel the common factor of $13$ .

Factor $13$ out of $- 13 j$ .

$\frac{- 1}{13} (13 (- j)) = - \frac{6}{13} \cdot - 13$

Cancel the common factor.

$\frac{- 1}{13} (13 (- j)) = - \frac{6}{13} \cdot - 13$

Rewrite the expression.

$- - j = - \frac{6}{13} \cdot - 13$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 j = - \frac{6}{13} \cdot - 13$

Multiply $j$ by $1$ .

$j = - \frac{6}{13} \cdot - 13$

Simplify the right side.

Simplify $- \frac{6}{13} \cdot - 13$ .

Cancel the common factor of $13$ .

Move the leading negative in $- \frac{6}{13}$ into the numerator.

$j = \frac{- 6}{13} \cdot - 13$

Factor $13$ out of $- 13$ .

$j = \frac{- 6}{13} \cdot (13 (- 1))$

Cancel the common factor.

$j = \frac{- 6}{13} \cdot (13 \cdot - 1)$

Rewrite the expression.

$j = - 6 \cdot - 1$

Multiply $- 6$ by $- 1$ .

$j = 6$

Solve for j 3j-5=8+1/2j+1/3j

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