High School

Which number(s) below belong to the solution set of the inequality [tex]x + 10 < 50[/tex]? Check all that apply.

A. 84
B. 41
C. 50
D. 40
E. 39
F. 16

Answer :

To solve the inequality [tex]\( x + 10 < 50 \)[/tex], let's break it down into simple steps:

1. Rearrange the Inequality:
- Start by isolating [tex]\( x \)[/tex] on one side. You can do this by subtracting 10 from both sides of the inequality:
[tex]\[
x + 10 < 50 \implies x < 50 - 10
\][/tex]
- Simplifying gives:
[tex]\[
x < 40
\][/tex]

2. Evaluate Each Option:
- Now, we need to check which numbers satisfy [tex]\( x < 40 \)[/tex].

Here are the numbers to check:
- Option A: 84
- Since 84 is not less than 40, it does not satisfy the inequality.
- Option B: 41
- Since 41 is not less than 40, it does not satisfy the inequality.
- Option C: 50
- Since 50 is not less than 40, it does not satisfy the inequality.
- Option D: 40
- Since 40 is not less than 40, it does not satisfy the inequality (it should be strictly less than).
- Option E: 39
- Since 39 is less than 40, it satisfies the inequality.
- Option F: 16
- Since 16 is less than 40, it satisfies the inequality.

3. Solution Set:
- The numbers that satisfy the inequality [tex]\( x + 10 < 50 \)[/tex] are 39 and 16.

Therefore, the correct numbers from the given options that belong to the solution set are Option E (39) and Option F (16).

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