Questions: 4(t-1)-6t ≥ t+8

Solution Steps

To solve the inequality \(4(t-1) - 6t \geq t + 8\), we need to simplify and isolate \(t\) on one side of the inequality. Here are the high-level steps:

1. Distribute and combine like terms on the left side.
2. Move all terms involving \(t\) to one side and constant terms to the other side.
3. Solve for \(t\).

First, distribute the \(4\) on the left side of the inequality: \[ 4(t - 1) - 6t \geq t + 8 \implies 4t - 4 - 6t \geq t + 8 \] Combine like terms: \[ -2t - 4 \geq t + 8 \]

Add \(2t\) to both sides to isolate the terms involving \(t\): \[ -4 \geq 3t + 8 \]

Subtract \(8\) from both sides to isolate the term involving \(t\): \[ -12 \geq 3t \]

Divide both sides by \(3\) to solve for \(t\): \[ -\frac{12}{3} \geq t \implies -4 \geq t \implies t \leq -4 \]

Final Answer