Question

Solve the compound inequality and choose the correct answer below. Number line looks like -7+1<-3x+13 and -2x -5>-4x-1. numberline look like.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the compound inequality -7 + 1 < -3x + 13 and -2x - 5 > -4x - 1, we need to solve each inequality separately and then combine the results.

For the first inequality:
-7 + 1 < -3x + 13
-6 < -3x + 13
-6 - 13 < -3x
-19 < -3x
19/3 > x
x < 19/3

For the second inequality:
-2x - 5 > -4x - 1
2x > -4x + 4
6x > 4
x > 2/3

Combining the results:
x < 19/3 and x > 2/3
Therefore, the solution to the compound inequality is 2/3 < x < 19/3.

On the number line, it would look like this:
(-∞, 2/3)U(2/3, 19/3)U(19/3, ∞)