Solve for x 16x-3(4x+7)=6x-(2x+21)

$16 x - 3 (4 x + 7) = 6 x - (2 x + 21)$

Step 1

Simplify $16 x - 3 (4 x + 7)$ .

Simplify each term.

Apply the distributive property.

$16 x - 3 (4 x) - 3 \cdot 7 = 6 x - (2 x + 21)$

Multiply $4$ by $- 3$ .

$16 x - 12 x - 3 \cdot 7 = 6 x - (2 x + 21)$

Multiply $- 3$ by $7$ .

$16 x - 12 x - 21 = 6 x - (2 x + 21)$

Subtract $12 x$ from $16 x$ .

$4 x - 21 = 6 x - (2 x + 21)$

Step 2

Simplify $6 x - (2 x + 21)$ .

Simplify each term.

Apply the distributive property.

$4 x - 21 = 6 x - (2 x) - 1 \cdot 21$

Multiply $2$ by $- 1$ .

$4 x - 21 = 6 x - 2 x - 1 \cdot 21$

Multiply $- 1$ by $21$ .

$4 x - 21 = 6 x - 2 x - 21$

Subtract $2 x$ from $6 x$ .

$4 x - 21 = 4 x - 21$

Step 3

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

Subtract $4 x$ from both sides of the equation.

$4 x - 21 - 4 x = - 21$

Combine the opposite terms in $4 x - 21 - 4 x$ .

Subtract $4 x$ from $4 x$ .

$0 - 21 = - 21$

Subtract $21$ from $0$ .

$- 21 = - 21$

Step 4

Since $- 21 = - 21$ , the equation will always be true for any value of $x$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$