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

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

Simplify $4 (- 6 + 3 x)$ .

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply.

Multiply $4$ by $- 6$ .

$- 24 + 4 (3 x) > 4 x + 8$

Multiply $3$ by $4$ .

$- 24 + 12 x > 4 x + 8$

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

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

$- 24 + 12 x - 4 x > 8$

Subtract $4 x$ from $12 x$ .

$- 24 + 8 x > 8$

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

Add $24$ to both sides of the inequality.

$8 x > 8 + 24$

Add $8$ and $24$ .

$8 x > 32$

Divide each term in $8 x > 32$ by $8$ and simplify.

Divide each term in $8 x > 32$ by $8$ .

$\frac{8 x}{8} > \frac{32}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} > \frac{32}{8}$

Divide $x$ by $1$ .

$x > \frac{32}{8}$

Simplify the right side.

Divide $32$ by $8$ .

$x > 4$

The result can be shown in multiple forms.

Inequality Form:

$x > 4$

Interval Notation:

$(4, \infty)$