Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

Starting with the first inequality:
-7 + 1 < -3x + 13
-6 < -3x + 13
Subtract 13 from both sides:
-19 < -3x
Divide by -3 (remember to reverse the inequality when dividing by a negative number):
19/3 > x
x < 19/3 or x < 6.33

Now, solving the second inequality:
-2x - 5 > -4x - 1
Add 4x to both sides:
2x - 5 > -1
Add 5 to both sides:
2x > 4
Divide by 2:
x > 2

Now, combining the two solutions:
Since x must satisfy both inequalities simultaneously, the solution is:
x < 6.33 and x > 2

So, the correct answer choice is: 2 < x < 6.33