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

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

Step 1

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

Simplify each term.

Apply the distributive property.

$3 x + 3 \cdot - 4 + 4 x < 7 x + 2$

Multiply $3$ by $- 4$ .

$3 x - 12 + 4 x < 7 x + 2$

Add $3 x$ and $4 x$ .

$7 x - 12 < 7 x + 2$

Step 2

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

Subtract $7 x$ from both sides of the inequality.

$7 x - 12 - 7 x < 2$

Combine the opposite terms in $7 x - 12 - 7 x$ .

Subtract $7 x$ from $7 x$ .

$0 - 12 < 2$

Subtract $12$ from $0$ .

$- 12 < 2$

Step 3

Since $- 12 < 2$ , the inequality will always be true.

Always true

Step 4

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$