Solve 3(4-2z)geq-11

$$3 ( 4 - 2 z ) \geq - 11$$

Solve for z

$$z\leq \frac{23}{6}$$

Solution Steps

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$4-2z\geq -\frac{11}{3}$$

Subtract 4 from both sides.

$$-2z\geq -\frac{11}{3}-4$$

Convert 4 to fraction \frac{12}{3}.

$$-2z\geq -\frac{11}{3}-\frac{12}{3}$$

Since -\frac{11}{3} and \frac{12}{3} have the same denominator, subtract them by subtracting their numerators.

$$-2z\geq \frac{-11-12}{3}$$

Subtract 12 from -11 to get -23.

$$-2z\geq -\frac{23}{3}$$

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

$$z\leq \frac{-\frac{23}{3}}{-2}$$

Express \frac{-\frac{23}{3}}{-2} as a single fraction.

$$z\leq \frac{-23}{3\left(-2\right)}$$

Multiply 3 and -2 to get -6.

$$z\leq \frac{-23}{-6}$$

Fraction \frac{-23}{-6} can be simplified to \frac{23}{6} by removing the negative sign from both the numerator and the denominator.

$$z\leq \frac{23}{6}$$