Question

What is the solution to the inequality |x-4| less than 3?

A: -7 less than x less than -1.
B: 1 less than x less than 7.
c: x less than -7 or x less than -1.
D: x greater than 1 or x less than 7.

Answer 1

b

Explanation:

Answer 2

B

Explanation:

x cannot have any negative value, or the sum with -4 will create -5 or lower, and the corresponding absolute value is therefore larger than 3.

so, A and C are automatically out.

D can't be right, because it is an "or" condition, so, we could violate one of the conditions (like "x greater than 1"), and it would still be OK, as long as we keep the second. but that is not true, as we just ruled out negative x values.

so, only B includes the "and" condition.

it means 1 has to be less than x AND x has to be less than 7.

and that is correct.