Solve -6(2x-3)leq-3(2-x)

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

Solve for x

$$x\geq \frac{8}{5}$$

Solution Steps

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

$$-12x+18\leq -3\left(2-x\right)$$

Use the distributive property to multiply -3 by 2-x.

$$-12x+18\leq -6+3x$$

Subtract 3x from both sides.

$$-12x+18-3x\leq -6$$

Combine -12x and -3x to get -15x.

$$-15x+18\leq -6$$

Subtract 18 from both sides.

$$-15x\leq -6-18$$

Subtract 18 from -6 to get -24.

$$-15x\leq -24$$

Divide both sides by -15. Since -15 is negative, the inequality direction is changed.

$$x\geq \frac{-24}{-15}$$

Reduce the fraction \frac{-24}{-15} to lowest terms by extracting and canceling out -3.

$$x\geq \frac{8}{5}$$