Solve the compound inequality 4 less than 2x minus 8, which is less than or equal to 10.
AThe interval [6, 9)
BThe interval (2, 5]
CThe interval (6, 9]
DThe interval (6, 18]
Answer & Solution
Correct answer: C. The interval (6, 9]
1. A compound inequality can be solved by working on all three parts at once.
2. Add 8 to every part to undo the subtraction.
3. That turns 4 into 12, leaves 2x in the middle, and turns 10 into 18.
4. Now divide every part by 2.
5. That gives 6 on the left, x in the middle, and 9 on the right.
6. The left sign was strictly less than, so 6 is left out and takes a parenthesis.
7. The right sign was less than or equal to, so 9 is included and takes a bracket.
8. The solution is therefore the interval from 6 to 9, written (6, 9].
9. The interval [6, 9) swaps the two endpoint symbols.
10. The interval (6, 18] forgets the final division by 2 on the right end.
_Source: OpenStax College Algebra (CC BY 4.0), section 2.7 Linear Inequalities and Absolute Value Inequalities_
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