Which number line represents the solution set for the inequality –4(x + 3) ≤ –2 – 2x?

Question

A number line from negative 7 to 7 in increments of 1. A point is at negative 5 and a bold line starts at negative 5 and is pointing to the right.
A number line from negative 7 to 7 in increments of 1. A point is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 7 to 7 in increments of 1. A point is at 5 and a bold line starts at 5 and is pointing to the left.
A number line from negative 7 to 7 in increments of 1. A point is at negative 5 and a bold line starts at negative 5 and is pointing to the right.

Answer 1

To solve the inequality \(-4(x + 3) \leq -2 - 2x\), we can first simplify it.

1. Distribute the \(-4\): \[ -4x - 12 \leq -2 - 2x \]

2. Next, add \(4x\) to both sides: \[ -12 \leq -2 + 2x \]

3. Now, add \(2\) to both sides: \[ -10 \leq 2x \]

4. Finally, divide both sides by \(2\): \[ -5 \leq x \] or equivalently, \[ x \geq -5 \]

The solution set is represented as \(x \geq -5\), which means the solution starts at \(-5\) and extends to the right toward positive infinity.

Therefore, looking at the number line choices:

• The number line that shows a bold line starting at \(-5\) and pointing to the right represents the correct solution set.

Thus, the correct representation is: A number line from negative 7 to 7 in increments of 1. A point is at negative 5 and a bold line starts at negative 5 and is pointing to the right.