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Chapter 2: Q 305 (page 183)

In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.

  1. b+78鈮�16
  2. 6y<48
  3. 40<58k

Short Answer

Expert verified

(a) The solution interval for inequality (a) is [-1724,鈭�)and representation on number line is :-

(b)The solution interval for inequality (b) is -鈭�,8and representation on number line is :-

(c) The solution interval for inequality (c) is 64,鈭�and representation on number line is :-

Step by step solution

01

Step 1. Part (a) Given and Solution

We have given the following inequality :-

b+78鈮�16

To solve the inequality subtract 78from both sides, then we have :-

b+78-78鈮�16-78鈬�b鈮�-1724

So the solution interval is [-1724,鈭�).

Representation of solution on number line is as following :-

02

Step 2. Part (b) Given and solution

Here we have the following inequality :-

6y<48.

To solve this inequality divide both sides by 6, then we have :-

6y6<486鈬�y<8

So the solution interval for this inequality is :-

-鈭�,8.

Representation of solution on number line is as following :-

03

Step 3. Part (c) Given and Solution

Now we have following inequality :-

40<58k

To solve the inequality multiply both sides by 85, then we have :-

40*85<58k*85鈬�64<kork>64

So the solution interval is 64,鈭�.

Representation of solution on number line is as following :-

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