Izzie is trying to solve this inequality: 3(t+1)−4t≥−5
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
Izzie did not solve the inequality correctly. Let's review the steps and correct any mistakes:
Starting with the given inequality: 3(t+1)−4t≥−5
First, distribute 3 to the terms inside the parentheses:
3t + 3 - 4t ≥ -5
Next, combine like terms:
-t + 3 ≥ -5
Now, you need to isolate the variable t. To do this, we can subtract 3 from both sides of the inequality:
-t ≥ -5 - 3
-t ≥ -8
However, when we multiply or divide both sides of an inequality by a negative number, we need to flip the inequality sign. So, in the next step, we will multiply both sides of the inequality by -1, which means flipping the inequality sign:
-t * -1 ≤ -8 * -1
t ≤ 8
Therefore, the correct solution is t ≤ 8.
To solve the inequality 3(t+1)−4t≥−5, let's go through the steps one by one:
1. Distribute the 3 on the left side: 3t + 3 - 4t ≥ -5
This step is correct.
2. Combine like terms: -t + 3 ≥ -5
This step is also correct.
3. To isolate t, subtract 3 from both sides: -t ≥ -8
This step is correct.
4. Finally, to solve for t, remember that when you multiply or divide both sides of an inequality by a negative number, the inequality flips. So, divide both sides by -1: t ≥ 8
This step is correct.
Therefore, Izzie solved the inequality correctly, and the solution is t ≥ 8. Well done!