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.