Question

Hazel is trying to solve this inequality. After she solves it, she shows it to you, and she asks you if she did it correctly. This is the work she completed:
3(t+1)−4t≥−5
3(t+1)−4t≥−5

Step 1: 3t +3−4t≥−5

Step 2: −t+3≥−5

Step 3: −t≥−8

Step 4: t≥8


Part A: In which step did Hazel make a mistake?

Part B: How would you explain to Hazel what her mistake was, so she won't make the mistake again on a future test?

Answer 1

We need to see Hazel's work for simplifying an inequality and see if she had a mistake or not.

The answers are:

a) Step 4.

B) She did not change the direction of the inequality symbol.

a) Let's analyze each step:

She starts with:

3*(t + 1) - 4*t ≥ −5

Step 1:

3t +3−4t ≥ −5

Here what she does is distributing the first product, she goes from:

3*(t + 1) to 3*t + 3

Step 2:

−t+3≥−5

Here what she did is adding "3*t - 4*t = (3 - 4)*t = -t"

Step 3:

−t ≥ −8

Here she subtracts 3 in both sides.

Step 4:

t ≥ 8

Here is the mistake.

B)

Here what she does is multiplying by -1 in both sides, her mistake is that we multiply both sides by a negative number in an inequality, the direction of the inequality must change, so here is her error.

So what she actually should had is:

-t  ≥ -8

(-1)*(-t) ≤ (-1)*(-8)

t ≤ 8

If you want to learn more, you can read:

brainly.com/question/20271304