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Which number(s) below belong to the solution set of the inequality [tex]x + 6 < 38[/tex]? Check all that apply.

A. 70
B. 44
C. 88
D. 31
E. 26
F. 32

Answer :

Let's solve the inequality [tex]\( x + 6 < 38 \)[/tex] step by step:

1. Subtract 6 from both sides of the inequality to isolate [tex]\( x \)[/tex]:
[tex]\[
x + 6 - 6 < 38 - 6
\][/tex]

2. Simplify the inequality:
[tex]\[
x < 32
\][/tex]

Now, let's check each option to see if it satisfies this inequality ([tex]\( x < 32 \)[/tex]):

- A. 70: [tex]\( 70 < 32 \)[/tex]? No, 70 is not less than 32.
- B. 44: [tex]\( 44 < 32 \)[/tex]? No, 44 is not less than 32.
- C. 88: [tex]\( 88 < 32 \)[/tex]? No, 88 is not less than 32.
- D. 31: [tex]\( 31 < 32 \)[/tex]? Yes, 31 is less than 32.
- E. 26: [tex]\( 26 < 32 \)[/tex]? Yes, 26 is less than 32.
- F. 32: [tex]\( 32 < 32 \)[/tex]? No, 32 is not less than 32 (it's equal).

The numbers that belong to the solution set of the inequality [tex]\( x + 6 < 38 \)[/tex] are:

- D. 31
- E. 26

These are the numbers that are less than 32.

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