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

Answer 1

To solve the compound inequality -7 < -3x + 13 < 1, we need to first isolate the variable x in the middle of the inequality.

-7 < -3x + 13 < 1
Subtract 13 from all parts of the inequality:
-20 < -3x < -12
Now, divide by -3 to get x by itself:
20/3 > x > 4

So, the solution to the first compound inequality is 4 < x < 20/3.

Now, let's solve the second compound inequality -2x - 5 > -4x - 1:

-2x - 5 > -4x - 1
Add 4x to both sides:
2x - 5 > -1
Add 5 to both sides:
2x > 4
Divide by 2 to get x by itself:
x > 2

So, the solution to the second compound inequality is x > 2.

Therefore, the overall solution to the compound inequality is 4 < x < 20/3 and x > 2.

The number line would look like:

- - - - 2 - - - 4 - - - 20/3 - - - - ↑