Question

Write the following in interval notation:

−
1
≤
13
x
−
11
<
7

Answer 1

10/13 ≤ x < 18/13

Explanation:

-1 ≤ 13x - 11 < 7

If a ≤ u < b then a ≤ u and u < b

⇒ -1 ≤ 13x - 11 and 13x - 11 < 7

-1 ≤ 13x - 11

Add 11 to both sides: 10 ≤ 13x

Divide both sides by 13: 10/13 ≤ x

13x - 11 < 7

Add 11 to both sides: 13x < 18

Divide both sides by 13: x < 18/13

Combine the intervals

10/13 ≤ x < 18/13