Which of the following values are solutions to the inequality x, minus, 7, is less than, 5, question markx−7<5?

Question

I., 12, II., 5, III., 16
I.12II.5III.16
Answer
Multiple Choice Answers
NoneNone
I onlyI only
II onlyII only
III onlyIII only
I and III and II
I and IIII and III
II and IIIII and III
I, II and IIII, II and III

Answer 1

To solve the inequality \( x - 7 < 5 \), we can isolate \( x \) as follows:

1. Add 7 to both sides of the inequality: \[ x - 7 + 7 < 5 + 7 \] Simplifying this yields: \[ x < 12 \]

Now we check which of the provided values satisfy this inequality:

• I. \( 12 \): Does not satisfy \( x < 12 \) (not a solution).
• II. \( 5 \): Satisfies \( 5 < 12 \) (is a solution).
• III. \( 16 \): Does not satisfy \( x < 12 \) (not a solution).

Based on our evaluation, only value II satisfies the inequality.

The answer is II only.