Question

. 5 < x – 2 < 11

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the compound inequality 5 < x - 2 < 11, we will first add 2 to all the parts of the inequality:

5 + 2 < x - 2 + 2 < 11 + 2

This simplifies to:

7 < x < 13

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the inequality 5 < x - 2 < 11, we can break it down into two separate inequalities:

1. x - 2 > 5
2. x - 2 < 11

Now, let's solve each inequality step-by-step:

1. x - 2 > 5:
Add 2 to both sides of the inequality:
x - 2 + 2 > 5 + 2
Simplify:
x > 7

2. x - 2 < 11:
Add 2 to both sides of the inequality:
x - 2 + 2 < 11 + 2
Simplify:
x < 13

So, the solution to the original inequality 5 < x - 2 < 11 is 7 < x < 13.

Answer 3

[AI-generated answer — Explain Bot]

To solve the inequality 5 < x - 2 < 11, we need to isolate the variable x.

First, let's add 2 to all parts of the inequality:

5 + 2 < x - 2 + 2 < 11 + 2

This simplifies to:

7 < x < 13

So, the solution to the inequality is x is greater than 7 and less than 13.

To understand how I arrived at this answer, we can go through the steps:

1. Start with the given inequality: 5 < x - 2 < 11
2. Add 2 to all parts of the inequality: 5 + 2 < x - 2 + 2 < 11 + 2
3. Simplify: 7 < x < 13

By adding 2 to both sides of the inequality, we shifted the entire inequality to the right by 2 units. Now x - 2 becomes x, and the 5 and 11 become 7 and 13, respectively. This gives us the solution that x is between 7 and 13, excluding the endpoints.