Solve 2(4-x)leq3(2x+6)-4

$$2 ( 4 - x ) \leq 3 ( 2 x + 6 ) - 4$$

Solve for x

$$x\geq -\frac{3}{4}$$

Solution Steps

Use the distributive property to multiply 2 by 4-x.

$$8-2x\leq 3\left(2x+6\right)-4$$

Use the distributive property to multiply 3 by 2x+6.

$$8-2x\leq 6x+18-4$$

Subtract 4 from 18 to get 14.

$$8-2x\leq 6x+14$$

Subtract 6x from both sides.

$$8-2x-6x\leq 14$$

Combine -2x and -6x to get -8x.

$$8-8x\leq 14$$

Subtract 8 from both sides.

$$-8x\leq 14-8$$

Subtract 8 from 14 to get 6.

$$-8x\leq 6$$

Divide both sides by -8. Since -8 is negative, the inequality direction is changed.

$$x\geq \frac{6}{-8}$$

Reduce the fraction \frac{6}{-8} to lowest terms by extracting and canceling out 2.

$$x\geq -\frac{3}{4}$$