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Chapter 6: Problem 33

Solve each inequality and graph the solution set on a number line. \(-3 x \geq-15\)

Short Answer

Expert verified
The solution to the inequality is \(x \leq 5\).

Step by step solution

01

Isolate the Variable

On the left side of the inequality is \(-3x\), and on the right side is \(-15\). To isolate \(x\), the \(-3\) on the left side needs to be removed. This is done by dividing both sides of the inequality by \(-3\). Remember, division by a negative number reverses the direction of the inequality sign.
02

Reverse the Inequality Sign

After dividing both sides by \(-3\), we get \(x \leq 5\). The sign has been reversed, as it should when we divide or multiply by a negative number.
03

Draw the Solution Set on Number Line

For this step, we need to draw a number line. A filled dot will be placed on \(5\) because the inequality \(x \leq 5\) includes \(5\). The line extends to the left, indicating that the solution includes all numbers less than or equal to \(5\) on the number line.

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