Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. solve for x and choose the correct solution: x - 3 ≤ -5

Explanation:

Step1: Solve the inequality

To solve \( x - 3 \leq -5 \), add 3 to both sides of the inequality.
\( x - 3 + 3 \leq -5 + 3 \)
Simplifying both sides, we get \( x \leq -2 \)? Wait, no, wait: \( -5 + 3 = -2 \)? Wait, no, \( -5 + 3 = -2 \)? Wait, no, \( -5 + 3 = -2 \)? Wait, no, let's recalculate: \( -5 + 3 = -2 \)? Wait, no, \( -5 + 3 = -2 \)? Wait, no, \( -5 + 3 = -2 \)? Wait, no, I made a mistake. Wait, \( x - 3 \leq -5 \). Add 3 to both sides: \( x \leq -5 + 3 \), which is \( x \leq -2 \)? Wait, no, \( -5 + 3 = -2 \)? Wait, no, \( -5 + 3 = -2 \)? Wait, no, \( -5 + 3 = -2 \)? Wait, no, that's correct? Wait, no, wait, \( -5 + 3 = -2 \). Wait, but let's check the number line. Wait, the first option is \( x \leq -8 \) with a closed dot at -8, the second is \( x \leq -2 \) with a closed dot at -2, the third is \( x \leq -2 \) with an open dot at -2, the fourth is \( x \leq -8 \) with an open dot at -8. Wait, no, let's re-solve the inequality.

Wait, the inequality is \( x - 3 \leq -5 \). Adding 3 to both sides: \( x \leq -5 + 3 \), so \( x \leq -2 \). Now, the inequality is "less than or equal to", so the dot should be closed (filled). Now, looking at the number lines:

• First number line: \( x \leq -8 \), closed dot at -8.
• Second number line: \( x \leq -2 \), closed dot at -2.
• Third number line: \( x \leq -2 \), open dot at -2.
• Fourth number line: \( x \leq -8 \), open dot at -8.

Since the solution is \( x \leq -2 \) with a closed dot (because the inequality is "≤"), the correct number line is the second one (the one with \( x \leq -2 \) and a closed dot at -2).

Wait, but let's recheck the calculation. \( x - 3 \leq -5 \). Add 3 to both sides: \( x \leq -5 + 3 \), so \( x \leq -2 \). Yes, that's correct. So the solution is \( x \leq -2 \), and since it's "≤", the dot is closed. So the second number line (from the left, the one with the closed dot at -2 and the arrow to the left) is correct.

Step2: Identify the correct number line

Now, we need to match the solution \( x \leq -2 \) with a closed dot (since "≤" includes the endpoint) to the number lines. The second number line (the one with \( x \leq -2 \) and a closed dot at -2) is the correct one.

Answer:

The second number line (from the left) with \( x \leq -2 \) and a closed dot at -2. (If we consider the options as labeled, assuming the first is leftmost: the second option, e.g., if the options are A, B, C, D from left to right, then B. \( x \leq -2 \) with a closed dot at -2)