Question

Eduardo solved the following inequality, and his work is shown below:

−5(x + 4) + 21 ≥ −3 + 4(x − 8)
−5x − 20 + 21 ≥ −3 + 4x − 32
−5x + 1 ≥ 4x − 35
−9x ≥ −36
x ≥ 4

What mistake did Eduardo make in solving the inequality?

When dividing by −9, he did not change the ≥ to ≤.

He subtracted 4x from both sides when he should have added 5x.

He subtracted 1 from both sides when he should have added 36.

He did not make a mistake.

Answer 1

why

Answer 2

The answer is A.

When you divide by a negative number you have to switch the sign.

Answer 3

1. -2x + 5 < 7
Subtract 5 from both sides, inequality side won't change
-2x < 2
Divide both sides by 2, inequality won't change sign now either
-x < 1
Multiply by -1, inequality will change sign
x > -1

2. 3 - (2x - 5) < -4(x + 2)
First, let's simplify it all we can
3 - 2x + 5 < -4x - 8
-2x + 8 < -4x - 8
Divide both sides by 2
-x + 4 < -2x - 4
Subtract 4 from both sides,
-x < -2x - 8
Add x to both sides,
0 < -x - 8
Add 8 to both sides,
8 < -x
Or,
x > -8

3. -5(x + 4) + 21 ≥ -3 + 4(x - 8)
-5x - 20 + 21 ≥ -3 + 4x - 32
-5x + 1 ≥ 4x - 35
-9x ≥ -36
x ≥ 1 <- Right over here, he did something that I don't understand really. Anyone?

Answer 4

is a

Answer 5

Yes