Questions: Solve. Write your answer in interval notation. -16x - 4 ≥ -5(x - 1)

Solution Steps

To solve the inequality \(-16x - 4 \geq -5(x - 1)\), we need to follow these steps:

1. Distribute the \(-5\) on the right-hand side.
2. Move all terms involving \(x\) to one side of the inequality.
3. Move all constant terms to the other side.
4. Solve for \(x\).
5. Write the solution in interval notation.

First, we need to distribute the \(-5\) on the right-hand side of the inequality: \[ -16x - 4 \geq -5(x - 1) \] \[ -16x - 4 \geq -5x + 5 \]

Next, we add \(5x\) to both sides to move all \(x\)-terms to the left side: \[ -16x + 5x - 4 \geq 5 \] \[ -11x - 4 \geq 5 \]

Now, we add \(4\) to both sides to isolate the \(x\)-term: \[ -11x - 4 + 4 \geq 5 + 4 \] \[ -11x \geq 9 \]

Finally, we divide both sides by \(-11\). Remember to reverse the inequality sign when dividing by a negative number: \[ x \leq \frac{9}{-11} \] \[ x \leq -\frac{9}{11} \]

Final Answer