Which of the following equations are equivalent to $| 7 x - 6 | + 4 = 9$ ?
A) $7 x - 2 = - 9$ or $7 x - 2 = 9$
B) $7 x - 2 = 9$
C) $7 x - 6 = - 5$ or $7 x - 6 = 5$
D) $7 x + 6 = - 5$ or $7 x + 6 = 5$

Question

Quizplus · Accepted Answer

We want to isolate the absolute value term, so we first subtract 4 from both sides to get $|7x-6|=5$. Then, we can break it down into two cases: ${7x-6}=5$ or ${7x-6}=-5$. Solving for x in each case gives us $x=\frac{11}{7}$ or $x=\frac{1}{7}$. This matches answer choice C. Answer choices A and D do not give us correct solutions for either equation in the absolute value, and answer choice B only gives us one solution.

Which of the Following Equations Are Equivalent To ∣7x−6∣+4=9| 7 x - 6 | + 4 = 9∣7x−6∣+4=9

Which of the Following Equations Are Equivalent To $| 7 x - 6 | + 4 = 9$