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Chapter 6: Problem 63

Solve each inequality and graph the solution set on a number line. \(-11<2 x-1 \leq-5\)

Short Answer

Expert verified
The acceptable values of \(x\) in the given inequality are \( -5< x \leq -2 \).

Step by step solution

01

Remove Subtract 1 on Inequalities

To make \(2x\) the subject, add 1 from both sides of the inequality: \[ -11 +1< 2x -1 +1 \leq -5 + 1 \], which simplifies to \[-10 < 2x \leq -4 \]. This step adheres to the basic principle that the same value should be added or subtracted from both sides of an inequality.
02

Simplifying further

To isolate \(x\), divide all parts of the inequality by 2 to get \[ -5 < x \leq -2 \]. Here, we maintain the inequality symbols since we divided by a positive number.
03

Graphing the Solution Set

Now we will plot the solution on the number line. We need to note that the < symbol indicates open circle (-5) on the number line. On the other hand, the 鈮� symbol refers to a closed circle at -2. The values of \(x\) lie between these two points.

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