Question

solve and graph the following inequality. provide an answer as a simplified fraction or mixed number. inequality: 5 - 2/3 > 19/3

Explanation:

Step1: Simplify the inequality

Multiply both sides of the inequality \(\frac{5}{3}-\frac{z}{2}>\frac{19}{3}\) by \(6\) (the least - common multiple of \(2\) and \(3\)) to get rid of the fractions.

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Step2: Isolate the variable term

Subtract \(10\) from both sides of the inequality \(10 - 3z>38\).

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Step3: Solve for \(z\)

Divide both sides of the inequality \(-3z>28\) by \(-3\). Remember that when dividing an inequality by a negative number, the direction of the inequality sign changes.

$$z<-\frac{28}{3}=-9\frac{1}{3}$$

Answer:

The solution of the inequality is \(z < - 9\frac{1}{3}\). To graph it, draw an open circle at \(-9\frac{1}{3}\) (because the inequality is strict, i.e., \(z\) is not equal to \(-9\frac{1}{3}\)) on the number line and shade the part of the number line to the left of \(-9\frac{1}{3}\).