In the inequality, what are all the possible values of x?

Question

-8x + 6 ≤ 2(-3x + 1)

Answer 1

To solve the inequality \(-8x + 6 ≤ 2(-3x + 1)\), we start by simplifying the right side.

1. Distribute the 2 on the right side: \[ 2(-3x + 1) = -6x + 2 \]

2. Now, rewrite the inequality: \[ -8x + 6 ≤ -6x + 2 \]

3. Next, let's isolate \(x\). Start by adding \(6x\) to both sides: \[ -8x + 6 + 6x ≤ 2 \] which simplifies to: \[ -2x + 6 ≤ 2 \]

4. Now subtract 6 from both sides: \[ -2x ≤ 2 - 6 \] simplifying to: \[ -2x ≤ -4 \]

5. Finally, divide both sides by \(-2\). Remember that when you divide by a negative number, you must flip the inequality sign: \[ x ≥ 2 \]

So, the solution to the inequality is: \[ x ≥ 2 \]

In interval notation, the solution set is: \[ [2, \infty) \]

Therefore, all possible values of \(x\) are \(x \geq 2\).