CA Foundation · Quantitative Aptitude · Linear Inequalities
A student is told that x is a real number with −2x ≤ 10 and x < 4. Which of the following describes all such x?
The correct description is −5 ≤ x < 4. Dividing −2x ≤ 10 by the negative number −2 reverses the inequality to x ≥ −5, and combining this with x < 4 gives the interval, which includes −5 but excludes 4.
- Ax ≤ −5 and x < 4
- B−5 ≤ x < 4Correct
- Cx ≥ 5 and x < 4
- D−5 < x ≤ 4
Explanation
Dividing −2x ≤ 10 by −2 reverses the sign, giving x ≥ −5. Combined with x < 4, we get −5 ≤ x < 4. Option x ≤ −5 forgets to reverse the sign. Option −5 < x ≤ 4 swaps which endpoints are included.
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