Question

3) |x-1|>15 4)|x+2|<11​

Answer 1

3) |x-1|>15

x - 1 > 15

x - 1 < -15

--

x > 16

x < -14

x∈ (-∞,-14) U(16, +∞)

4)|x+2|<11​

x + 2 < 11

x + 2 > -11

--

x < 9

x > -13

x∈ (-13, 9)

Answer 2

To solve the absolute value inequalities you provided, let's analyze each one separately:

3. |x - 1| > 15

To solve this inequality, we need to consider two cases:

Case 1: (x - 1) > 15 Solving for x: x > 16

Case 2: -(x - 1) > 15 Solving for x: -x + 1 > 15 -x > 14 x < -14 (Remember to flip the inequality when multiplying or dividing by a negative number.)

Therefore, the solution to the inequality |x - 1| > 15 is x < -14 or x > 16.

4. |x + 2| < 11

To solve this inequality, we again consider two cases:

Case 1: (x + 2) < 11 Solving for x: x < 9

Case 2: -(x + 2) < 11 Solving for x: -x - 2 < 11 -x < 13 x > -13 (Remember to flip the inequality when multiplying or dividing by a negative number.)

Therefore, the solution to the inequality |x + 2| < 11 is -13 < x < 9.

In summary:

• The solution to |x - 1| > 15 is x < -14 or x > 16.
• The solution to |x + 2| < 11 is -13 < x < 9.