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

  1. -1<x<3
  2. -3<x≤-2
  3. -1.25≤x≤0

Short Answer

Expert verified

(a)The solution interval for inequality (a) is -1,3and representation on number line is :-

(b)The solution interval for inequality (b) is (-3,-2]and representation on number line is :-

(c) The solution interval for inequality (c) is -1.25,0and representation on number line is :-

Step by step solution

01

Step 1. Part (a) Given and Solution

We have given the following inequality :-

-1<x<3.

Every value greater than -1 and less than 3 is the solution of this inequality.

So solution interval is :-

-1,3.

Representation of solution of number line is as following :-

02

Step 2. Part (b) Given and Solution

Here we have given the following inequality :-

-3<x≤-2.

Every value greater than -3 and less than or equals to -2 is solution of this inequality.

So the solution interval is :- (-3,-2].

Representation of solution on number line is as following :-

03

Step 3. Part (c) Given and Solution

Now we have following inequality :-

1.25≤x≤0.

Every value greater than or equal to -1.25 and less than or equals to 0 is the solution of this inequality.

So solution interval for this inequality is :-

-1.25,0.

Representation of solution on number line is as following :-

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