Question

Please help, I'm running out of points.

Solve for x: −6 < x − 1 < 9
5 < x < 10
−5 < x < 10
−5 > x > 10
5 > x > −10

Answer 1

−5 < x < 10

Explanation:

Add 1 to each part of the three parts of the inequality:

-6 +1 < x - 1 +1 < 9 +1

-5 < x < 10 . . . . . simplify

_____

The only place where there's an x is in the middle section. The only operation performed on x is subtraction of 1. To undo that subtraction, you add 1, but you must add 1 to all sides of the comparison symbols in order to keep them true.

Such a compound inequality is the same as the two inequalities:

• -6 < x-1
• x-1 < 9

Solving either one of these is done by adding 1 to both sides of the < symbol:

• -5 < x
• x < 10

You can put these back together in the form of the compound inequality ...

-5 < x < 10