Solve for j 8(j-4)=2(4j-16)

$8 (j - 4) = 2 (4 j - 16)$

Step 1

Simplify $8 (j - 4)$ .

Start simplifying.

$0 + 0 + 8 (j - 4) = 2 (4 j - 16)$

Simplify by adding zeros.

$8 (j - 4) = 2 (4 j - 16)$

Apply the distributive property.

$8 j + 8 \cdot - 4 = 2 (4 j - 16)$

Multiply $8$ by $- 4$ .

$8 j - 32 = 2 (4 j - 16)$

Step 2

Simplify $2 (4 j - 16)$ .

Apply the distributive property.

$8 j - 32 = 2 (4 j) + 2 \cdot - 16$

Multiply.

Multiply $4$ by $2$ .

$8 j - 32 = 8 j + 2 \cdot - 16$

Multiply $2$ by $- 16$ .

$8 j - 32 = 8 j - 32$

Step 3

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

Subtract $8 j$ from both sides of the equation.

$8 j - 32 - 8 j = - 32$

Combine the opposite terms in $8 j - 32 - 8 j$ .

Subtract $8 j$ from $8 j$ .

$0 - 32 = - 32$

Subtract $32$ from $0$ .

$- 32 = - 32$

Step 4

Since $- 32 = - 32$ , the equation will always be true for any value of $j$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$