Question

solve the inequality. graph the solution.

3x ≤ -\frac{5}{4}

the solution is □.

Explanation:

Step1: Divide both sides by 3

$$3x\leq-\frac{5}{4}$$
$$\frac{3x}{3}\leq\frac{-\frac{5}{4}}{3}$$

Step2: Simplify the right - hand side

$$x\leq-\frac{5}{4}\times\frac{1}{3}$$
$$x\leq-\frac{5}{12}$$

Answer:

$$x\leq-\frac{5}{12}$$

To graph the solution: Draw a number line. Place a closed circle at \(-\frac{5}{12}\) (because the inequality is \(\leq\)) and shade to the left of \(-\frac{5}{12}\) to represent all values of \(x\) that are less than or equal to \(-\frac{5}{12}\).