Solve the Inequality for x 4(3x-8)<6x+4

$4 (3 x - 8) < 6 x + 4$

Step 1

Simplify $4 (3 x - 8)$ .

Rewrite.

$0 + 0 + 4 (3 x - 8) < 6 x + 4$

Simplify by adding zeros.

$4 (3 x - 8) < 6 x + 4$

Apply the distributive property.

$4 (3 x) + 4 \cdot - 8 < 6 x + 4$

Multiply.

Multiply $3$ by $4$ .

$12 x + 4 \cdot - 8 < 6 x + 4$

Multiply $4$ by $- 8$ .

$12 x - 32 < 6 x + 4$

Step 2

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

Subtract $6 x$ from both sides of the inequality.

$12 x - 32 - 6 x < 4$

Subtract $6 x$ from $12 x$ .

$6 x - 32 < 4$

Step 3

Move all terms not containing $x$ to the right side of the inequality.

Add $32$ to both sides of the inequality.

$6 x < 4 + 32$

Add $4$ and $32$ .

$6 x < 36$

Step 4

Divide each term in $6 x < 36$ by $6$ and simplify.

Divide each term in $6 x < 36$ by $6$ .

$\frac{6 x}{6} < \frac{36}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} < \frac{36}{6}$

Divide $x$ by $1$ .

$x < \frac{36}{6}$

Simplify the right side.

Divide $36$ by $6$ .

$x < 6$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < 6$

Interval Notation:

$(- \infty, 6)$