Solve the Inequality for x 7x-(3x-4)>=2(x-6)

$7 x - (3 x - 4) \geq 2 (x - 6)$

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

Simplify each term.

Apply the distributive property.

$7 x - (3 x) - - 4 \geq 2 (x - 6)$

Multiply $3$ by $- 1$ .

$7 x - 3 x - - 4 \geq 2 (x - 6)$

Multiply $- 1$ by $- 4$ .

$7 x - 3 x + 4 \geq 2 (x - 6)$

Subtract $3 x$ from $7 x$ .

$4 x + 4 \geq 2 (x - 6)$

Simplify $2 (x - 6)$ .

Apply the distributive property.

$4 x + 4 \geq 2 x + 2 \cdot - 6$

Multiply $2$ by $- 6$ .

$4 x + 4 \geq 2 x - 12$

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

Subtract $2 x$ from both sides of the inequality.

$4 x + 4 - 2 x \geq - 12$

Subtract $2 x$ from $4 x$ .

$2 x + 4 \geq - 12$

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

Subtract $4$ from both sides of the inequality.

$2 x \geq - 12 - 4$

Subtract $4$ from $- 12$ .

$2 x \geq - 16$

Divide each term in $2 x \geq - 16$ by $2$ and simplify.

Divide each term in $2 x \geq - 16$ by $2$ .

$\frac{2 x}{2} \geq \frac{- 16}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \geq \frac{- 16}{2}$

Divide $x$ by $1$ .

$x \geq \frac{- 16}{2}$

Simplify the right side.

Divide $- 16$ by $2$ .

$x \geq - 8$

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 8$

Interval Notation:

$[- 8, \infty)$