Question

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

Answer 1

To solve the inequality \( 3(t+1) - 4t > -5 \), we can follow these steps:

1. Distribute the \(3\) in the expression:
\[
3(t + 1) = 3t + 3
\]
So the inequality becomes:
\[
3t + 3 - 4t > -5
\]

2. Combine like terms:
\[
(3t - 4t) + 3 > -5
\]
This simplifies to:
\[
-t + 3 > -5
\]

3. Subtract \(3\) from both sides to isolate the term with \(t\):
\[
-t > -5 - 3
\]
This simplifies to:
\[
-t > -8
\]

4. Multiply both sides by \(-1\). Remember that when multiplying or dividing by a negative number, the inequality sign flips:
\[
t < 8
\]

So the solution to the inequality is:
\[
t < 8
\]