Question

step 1 subtract 3.6 from both sides of the inequality.
-5.8 ≥ x + 3.6
-5.8 - 3.6 ≥ x + 3.6 - 3.6
-9.2 ≥ x
step 2 interpret the results.
x ≥ -9.2
x is greater than or equal to -9.2.
step 3 draw a number line.
number line with -9.5, -9.4, -9.3, -9.2 (blue arrow left from -9.2), -9.1, -9, -8.9, -8.8
which describes the first step in which marquis made an error?
○ in step 1, marquis should have added 3.6 to each side of the inequality.
○ in step 2, marquis should have interpreted the results as x ≤ -9.2, which means that x is less than or equal to -9.2.
○ marquis should have used an open circle at -9.2 in step 3.
○ marquis should have shaded the number line to the right of -9.2 in step 3.

Explanation:

• Analyze Step 1: Subtracting 3.6 from both sides of \(-5.8 \geq x + 3.6\) gives \(-5.8 - 3.6 \geq x + 3.6 - 3.6\), which simplifies to \(-9.4 \geq x\)? Wait, no, original calculation in Step 1 is \(-5.8 - 3.6=-9.4\)? Wait, no, the user's Step 1 shows \(-5.8 - 3.6=-9.2\), which is a calculation error? Wait, no, the question is about the interpretation or steps. Wait, Step 2: The inequality from Step 1 is \(-9.2 \geq x\), which is equivalent to \(x \leq -9.2\), not \(x \geq -9.2\). So Marquis made an error in Step 2 by misinterpreting the inequality direction.
• Check other options:
• Step 1: Subtracting 3.6 from both sides is correct for solving \(x + 3.6\) (to isolate \(x\)), so the first option is wrong.
• Step 3: Since the inequality is \(x \leq -9.2\), a closed circle (because of "equal to") at \(-9.2\) and shading to the left is correct, so the third and fourth options are wrong.
• Step 2: The correct interpretation of \(-9.2 \geq x\) is \(x \leq -9.2\) (x is less than or equal to -9.2), so Marquis's interpretation here is wrong.

Answer:

B. In Step 2, Marquis should have interpreted the results as \(x \leq -9.2\), which means that \(x\) is less than or equal to \(-9.2\).