can someone SHOW me how to solve these graphs?2x > -6 and x - 4 < 3

Question

x + 5 > 2x + 1 and -4x < -8

-6 < x + 3 < 6 (Remember this is an "and" statement)

-3x < -6 or x + 5 < -2

x - 2 > 2x + 1 or -10 > -2x - 2

Look at the third.
-6 < x + 3 < 6 (Remember this is an "and" statement)

so x+3 is greater than -6, or
x is greater than -3. So to the right of -3 is allowed, but we have a second conditon: x+3 is les than six. or x is less than 3.

so the allowed solution is between -3 and 3.

I will be happy to critique your thinking on the others.

Look at the third.
-6 < x + 3 < 6 (Remember this is an "and" statement)

so x+3 is greater than -6, or
x is greater than -3. So to the right of -3 is allowed, but we have a second conditon: x+3 is les than six. or x is less than 3.

so the allowed solution is between -3 and 3.

I will be happy to critique your thinking on the others.