Solve the inequality. So i have done this problem at least three times and I keep getting the same answer. But in the back of the book the correct answer for this problem is x<or equal to 5

This is what I did & my answer dosen't match the one in the back of the book:

-9(x-3)-8(4-x)> or equal to -2x
-9x+27-32+8 > or equal to -2x
-9x+3 > or equal to -2x
added 9x to both sides
3> or equal to 7x
divided both sides by 7
My answer: x< or equal to 7/3

you should have a 8x, not 8 in your second line

the second line of your equation you did not multiple the 8 times the x, you just multiplied by the 4

STOP!!!!!!!!!!!!!!!!!!!!!!

To solve the inequality, let's go through the steps:

-9(x - 3) - 8(4 - x) ≥ -2x

First, distribute the -9 and -8 on the left side:

-9x + 27 + 8x - 32 ≥ -2x

Combine like terms:

-x - 5 ≥ -2x

To isolate the variables on one side, subtract -x and add 2x to both sides:

-x + 2x - 5 ≥ -2x + 2x

Simplifying further:

x - 5 ≥ 0

Now, to solve for x, add 5 to both sides:

x - 5 + 5 ≥ 0 + 5

Simplifying:

x ≥ 5

Therefore, the correct answer is x ≥ 5.

It seems there might have been a mistake made when adding 9x to both sides. The equation should be:

-9x + 3 ≥ -2x

When 9x is added to both sides, it becomes:

3 ≥ 7x

And when dividing both sides by 7:

3/7 ≥ x

Which means x ≤ 3/7, not x ≤ 7/3.

So, to clarify, the correct answer is x ≥ 5, not x ≤ 7/3.