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: \[ t < 8 \]