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

It's "when dividing by −9, he did not change the ≥ to ≤."

Whenever you multiply or divide by a negative, the sign always flips to the opposite way.

Answer 2

Answer: The correct option is

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

Step-by-step explanation: Given that Eduardo solved an inequality as shown below :

`-5(x+4)+21\geq-3+4(x-8)\\\\\Rightarrow -5x-20+21 \geq-3+4x-32\\\\\Rightarrow-5x+1\geq4x-35\\\\\Rightarrow-9x\geq-36\\\\\Rightarrow x\geq 4.`

We are to check the mistake that Eduardo made in the above calculation.

We know that

if an inequality is multiplied by a negative sign, then the sign of the inequality changes.

That is,

`a\geq b~~~~~\Rightarrow -a\leq -b,\\\\a\leq b~~~~~\Rightarrow -a\geq -b.`

So, Eduardo made mistake in the last step. While dividing by -9, the sign of the inequality should change, i.e., ≥ to ≤.

Therefore, the correct calculation is:

`-5(x+4)+21\geq-3+4(x-8)\\\\\Rightarrow -5x-20+21 \geq-3+4x-32\\\\\Rightarrow-5x+1\geq4x-35\\\\\Rightarrow-9x\geq-36\\\\\Rightarrow x\leq 4.`

Option (A) is CORRECT.