Solve the compound inequality. Write the solution in interval notation.
-5x + 2

Question

Solve the compound inequality. Write the solution in interval notation.
-5x + 2 < 6x + 4 < 7x - 4
A)(-2, ∞)
B)(-2, 8)
C)(8, ∞)
D)(-∞, 8)

Quizplus · Accepted Answer

Subtracting 5x from all parts of the inequality gives:
2 < x + 4 < 2x - 4
Add -4 to all parts:
-2 < x < 2x - 8
Add -x to all parts:
-x - 2 < -8
Add 2 to all parts:
-x < -6
Multiply by -1 and flip the inequality:
x > 6
So the solution is (6, ∞), but since that is not an option, the closest choice is (8, ∞), which is answer choice C.

Solve the Compound Inequality