Solve for j 7j+1=4(-2j-5)+12j

$7 j + 1 = 4 (- 2 j - 5) + 12 j$

Step 1

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

$4 (- 2 j - 5) + 12 j = 7 j + 1$

Step 2

Simplify $4 (- 2 j - 5) + 12 j$ .

Simplify each term.

Apply the distributive property.

$4 (- 2 j) + 4 \cdot - 5 + 12 j = 7 j + 1$

Multiply $- 2$ by $4$ .

$- 8 j + 4 \cdot - 5 + 12 j = 7 j + 1$

Multiply $4$ by $- 5$ .

$- 8 j - 20 + 12 j = 7 j + 1$

Add $- 8 j$ and $12 j$ .

$4 j - 20 = 7 j + 1$

Step 3

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

Subtract $7 j$ from both sides of the equation.

$4 j - 20 - 7 j = 1$

Subtract $7 j$ from $4 j$ .

$- 3 j - 20 = 1$

Step 4

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

Add $20$ to both sides of the equation.

$- 3 j = 1 + 20$

Add $1$ and $20$ .

$- 3 j = 21$

Step 5

Divide each term in $- 3 j = 21$ by $- 3$ and simplify.

Divide each term in $- 3 j = 21$ by $- 3$ .

$\frac{- 3 j}{- 3} = \frac{21}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 j}{- 3} = \frac{21}{- 3}$

Divide $j$ by $1$ .

$j = \frac{21}{- 3}$

Simplify the right side.

Divide $21$ by $- 3$ .

$j = - 7$