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Chapter 2: Q. 2.147 (page 204)

Solve the below inequality, graph the solution and write the solution in interval notation:

2x-1≤5

Short Answer

Expert verified

The solution of the inequality is -2≤x≤3.

Interval notation: -2,3

Graph of the inequality is

Step by step solution

01

Step 1. Given Information.

We have:

2x-1≤5

02

Step 2. Write the equivalent compound inequality. 

2x-1≤5

Apply absolute rule: If |u| ≤ a, a > 0 then -a ≤ u ≤ a

-5≤ 2x-1≤ 5

03

Step 3. Solve the compound inequality. 

Break the compound inequality:

-5≤  2x-1and  2x-1≤  5

First, solve -5≤  2x-1:

Switch sides:

2x-1≥ -52x-1+1≥ -5+12x≥ -42x2≥-42x≥ -2

Now, solve   2x-1≤  5:

Add 1to both sides:

2x-1+1≤ 5+12x≤ 62x2≤62x≤ 3

Merge overlapping intervals:

-2≤ x≤ 3

Interval notation:-2,3

04

Step 4. Graph the solution. 

Plot the points -2and 3with a closed circle because it is included in the solution.

The graph of -2≤x≤3is shown below:

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