Solve -8(x+3)-4x+10geq-2(x+4)+5x-10

$$- 8 ( x + 3 ) - 4 x + 10 \geq - 2 ( x + 4 ) + 5 x - 10$$

Solve for x

$$x\leq \frac{4}{15}$$

Solution Steps

Use the distributive property to multiply -8 by x+3.

$$-8x-24-4x+10\geq -2\left(x+4\right)+5x-10$$

Combine -8x and -4x to get -12x.

$$-12x-24+10\geq -2\left(x+4\right)+5x-10$$

Add -24 and 10 to get -14.

$$-12x-14\geq -2\left(x+4\right)+5x-10$$

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

$$-12x-14\geq -2x-8+5x-10$$

Combine -2x and 5x to get 3x.

$$-12x-14\geq 3x-8-10$$

Subtract 10 from -8 to get -18.

$$-12x-14\geq 3x-18$$

Subtract 3x from both sides.

$$-12x-14-3x\geq -18$$

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

$$-15x-14\geq -18$$

Add 14 to both sides.

$$-15x\geq -18+14$$

Add -18 and 14 to get -4.

$$-15x\geq -4$$

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

$$x\leq \frac{-4}{-15}$$

Fraction \frac{-4}{-15} can be simplified to \frac{4}{15} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{4}{15}$$