Solve the inequality and give your answer in interval notation.

Question

Solve the inequality and give your answer in interval notation.

13 −2|5𝑥−1| ≤7

Please help solve.

Answer 1

First we'll want to simplify this equation a little bit:

13 - 2|5x-1| <= 7

-2|5x-1| <= -6

|5x-1| >= 3 (note that we have to swap the <= with >= because we're dividing by a negative number)

Now we can solve this inequality with two different equations: 5x-1 >= 3 and 5x-1 <= -3. Let's do the first one first:

5x-1 >= 3

5x >= 4

x >= 4/5

And now the second one:

5x-1 <= -3

5x <= -2

x <= -2/5

So the final answer is (-∞, -2/5] U [4/5, ∞).