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Chapter 0: Problem 31

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$-9 x \geq 36$$

Short Answer

Expert verified
The solution to the inequality is \(x \leq -4\) or in interval notation it is \((- \infty, -4]\).

Step by step solution

01

Solve the inequality

Start by isolating the variable on one side of the inequality. Divide both sides by -9 to get x. It should be noted that when dividing by a negative number, the direction of the inequality changes. Hence, -9x 鈮� 36 becomes \(x \leq -4\).
02

Convert to interval notation

The solution \(x \leq -4\) in interval notation becomes \((- \infty, -4]\).
03

Graph the solution set on the number line

Draw a number line, plot -4. The inequality \(x \leq -4\) implies that the solutions may be -4 or any number less than -4. This means we must darken the line to the left of -4 (including -4).

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. In an inequality such as \(5 x+4<8 x-5,\) I can avoid division by a negative number depending on which side I collect the variable terms and on which side I collect the constant terms.

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