Izzie is trying to solve this inequality: 3(t+1)−4t≥−5

Question

After she solves it, she shows it to you, and she asks you if she did it correctly.

This is the work she completed:

3t+3−4t≥−5
−t+3≥−5
−t≥−8
t≥8
(2 points)
True False
Izzie should not have changed the inequality symbol from ≥ to ≤

Answer 1

To determine whether Izzie solved the inequality correctly, let's go through her steps.

Starting with the original inequality: \[ 3(t+1) - 4t \geq -5 \]

1. Distributing the \(3\): \[ 3t + 3 - 4t \geq -5 \]

2. Combining like terms: \[ -t + 3 \geq -5 \]

3. Subtracting \(3\) from both sides: \[ -t \geq -8 \]

4. To solve for \(t\), multiply both sides by \(-1\). Remember that multiplying or dividing by a negative number reverses the inequality: \[ t \leq 8 \]

So the correct solution is: \[ t \leq 8 \]

Izzie concluded that \(t \geq 8\), which is incorrect. Therefore, her final answer is not correct.

In response to the statement "Izzie should not have changed the inequality symbol from ≥ to ≤":

• This statement is True. She made an error when changing the direction of the inequality after multiplying both sides by \(-1\).

So the answer to the original question is False, as Izzie did not solve it correctly and should have reversed the inequality symbol.