Solve -4z+31geq17z+23

$$- 4 z + 31 \geq 17 z + 23$$

Solve for z

$$z\leq \frac{8}{21}$$

Solution Steps

Subtract 17z from both sides.

$$-4z+31-17z\geq 23$$

Combine -4z and -17z to get -21z.

$$-21z+31\geq 23$$

Subtract 31 from both sides.

$$-21z\geq 23-31$$

Subtract 31 from 23 to get -8.

$$-21z\geq -8$$

Divide both sides by -21. Since -21 is negative, the inequality direction is changed.

$$z\leq \frac{-8}{-21}$$

Fraction \frac{-8}{-21} can be simplified to \frac{8}{21} by removing the negative sign from both the numerator and the denominator.

$$z\leq \frac{8}{21}$$