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Chapter 6: Problem 39

Solve each inequality and graph the solution set on a number line. \(-2 x-3<3\)

Short Answer

Expert verified
The solution to the inequality \(-2x-3<3\) is \(x > -3\). On the number line, the values corresponding to \(x > -3\) will be shaded.

Step by step solution

01

Isolate the variable

To isolate \(x\), first add 3 on both sides of the inequality to cancel out -3 on the left. It then yields \(-2x < 3 + 3\), which simplifies to \(-2x < 6\). Next, divide both sides of the inequality by -2. Remember, when dividing by a negative number, the inequality sign will flip. This simplifies to \(x > -3\).
02

Graph on a number line

Now, this result can be graphed on a number line. Using a number line, put a open circle on -3 and shade whatever is greater than -3. Since the inequality is concerned with values greater than -3, the shaded part should be on the right of -3.

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