Question

Solve the following inequalities: |2x−1| − 1 | 7x+3 |=8

a. x = -2, x = 3
b. x = 1, x = -4
c. x = -1, x = 2
d. x = 4, x = -3

Answer 1

To solve the inequality |2x−1| − 1 | 7x+3 |=8, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative. The correct solution is x=3.

Step-by-step explanation:

To solve the inequality |2x−1| − 1 | 7x+3 |=8, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

1. When 2x−1 is positive: In this case, the inequality becomes 2x−1-1-7x-3=8, which simplifies to x=-2. However, -2 doesn't satisfy the condition, so we discard this solution.
2. When 2x−1 is negative: In this case, the inequality becomes -(2x−1)-1-7x-3=8, which simplifies to x=3. Keeping in mind that we're considering the case where 2x-1 is negative, we keep this solution.

Therefore, the correct solution is x=3.