Solve 3z+7/-5leq4-z

$$\frac { 3 z + 7 } { - 5 } \leq 4 - z$$

Solve for z

$$z\leq \frac{27}{2}$$

Solution Steps

Multiply both sides of the equation by -5. Since -5 is negative, the inequality direction is changed.

$$3z+7\geq -20+5z$$

Subtract 5z from both sides.

$$3z+7-5z\geq -20$$

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

$$-2z+7\geq -20$$

Subtract 7 from both sides.

$$-2z\geq -20-7$$

Subtract 7 from -20 to get -27.

$$-2z\geq -27$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$z\leq \frac{-27}{-2}$$

Fraction \frac{-27}{-2} can be simplified to \frac{27}{2} by removing the negative sign from both the numerator and the denominator.

$$z\leq \frac{27}{2}$$