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

  1. a+34≥710
  2. 8x>72
  3. 20>25h

Short Answer

Expert verified

(a) The solution interval for inequality (a) is [-120,∞)and representation on number line is :-

(b)The solution interval for inequality (b) is 9,∞and representation on number line is :-

(c) The solution interval for inequality (c) is -∞,50and representation on number line is :-

Step by step solution

01

Step 1. Part (a) Given and Solution

We have given the following inequality :-

a+34≥710

Now to solve this inequality, subtract 34from both sides, then we have :-

a+34-34≥710-34⇒a≥-120

So the solution interval for this inequality is :-

[-120,∞).

Representation of solution on number line is as following :-

02

Step 2. Part (b) Given and solution

Here we have given the following inequality :-

8x>72.

To solve this inequality divide both sides by 8, then we have :-

8x8>728⇒x>9

So the solution interval is 9,∞.

Representation of solution on number line is as following :-

03

Step 3. Part (c) Given and solution

Now we have following inequality :-

20>25h.

To solve this inequality multiply both sides by 52, then we have :-

20*52>25h*52⇒50>horh<50

Then the solution interval is :-

-∞,50.

Representation of solution on number line is as following :-

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