MCQ
If $– 3x + 17 < – 13,$ then:
- ✓$\text{x}\in(10,\infty)$
- B$\text{x}\in\big[10,\infty)$
- C$\text{x}\in(-\infty,10\big]$
- D$\text{x}\in\big[-10,10)$
✓
Answer
Correct option: A.
$\text{x}\in(10,\infty)$
Given,
$-3x + 17 < -13$
Subtracting $17$ from both sides,
$-3x + 17 – 17 < -13 – 17$
$\Rightarrow -3x < -30$
$\Rightarrow x > 10 ($since the division by negative number inverts the inequality sign$)$
$\Rightarrow\text{x}\in(10,\infty)$
$-3x + 17 < -13$
Subtracting $17$ from both sides,
$-3x + 17 – 17 < -13 – 17$
$\Rightarrow -3x < -30$
$\Rightarrow x > 10 ($since the division by negative number inverts the inequality sign$)$
$\Rightarrow\text{x}\in(10,\infty)$
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