Which of the following inequalities is equivalent to $| 7 x - 9 | + 2 8$ A) $7 x - 9 6$ B) $7 x - 9 6$ C) $- 6 7 x - 9 6$ D) $7 x - 7 8$

Question

Which of the following inequalities is equivalent to $| 7 x - 9 | + 2 > 8$ A) $7 x - 9 > 6$ B) $7 x - 9 < - 6$ or $7 x - 9 > 6$ C) $- 6 > 7 x - 9 > 6$ D) $7 x - 7 < - 8$ or $7 x - 7 > 8$

Quizplus · Accepted Answer

First, we isolate the absolute value term by subtracting 2 from both sides: $$|7x-9|>6$$ Next, we split this inequality into two inequalities, one with a positive argument and one with a negative argument: $$7x-9>6 ext{ or }7x-9<-6$$ Which simplifies to: $$7x>15 ext{ or }7x<3$$ Finally, we write the solution set in interval notation: $$(x<\frac{3}{7} ext{ or }x>\frac{15}{7})$$ which is equivalent to choice B.

Which of the Following Inequalities Is Equivalent To ∣7x−9∣+2>8| 7 x - 9 | + 2 > 8∣7x−9∣+2>8

Which of the Following Inequalities Is Equivalent To $| 7 x - 9 | + 2 > 8$