Solve the Inequality for x 4(3x-2)-3x<3(1+3x)-7

$4 (3 x - 2) - 3 x < 3 (1 + 3 x) - 7$

Simplify $4 (3 x - 2) - 3 x$ .

Simplify each term.

Apply the distributive property.

$4 (3 x) + 4 \cdot - 2 - 3 x < 3 (1 + 3 x) - 7$

Multiply $3$ by $4$ .

$12 x + 4 \cdot - 2 - 3 x < 3 (1 + 3 x) - 7$

Multiply $4$ by $- 2$ .

$12 x - 8 - 3 x < 3 (1 + 3 x) - 7$

Subtract $3 x$ from $12 x$ .

$9 x - 8 < 3 (1 + 3 x) - 7$

Simplify $3 (1 + 3 x) - 7$ .

Simplify each term.

Apply the distributive property.

$9 x - 8 < 3 \cdot 1 + 3 (3 x) - 7$

Multiply $3$ by $1$ .

$9 x - 8 < 3 + 3 (3 x) - 7$

Multiply $3$ by $3$ .

$9 x - 8 < 3 + 9 x - 7$

Subtract $7$ from $3$ .

$9 x - 8 < 9 x - 4$

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

Subtract $9 x$ from both sides of the inequality.

$9 x - 8 - 9 x < - 4$

Combine the opposite terms in $9 x - 8 - 9 x$ .

Subtract $9 x$ from $9 x$ .

$0 - 8 < - 4$

Subtract $8$ from $0$ .

$- 8 < - 4$

Since $- 8 < - 4$ , the inequality will always be true.

Always true

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$