3
algebra

Which step contains the first error in solving 3−2x≤113 - 2x \leq 11? Step 1: −2x≤8-2x \leq 8 Step 2: x≤−4x \leq -4 Step 3: xx is any number less than or equal to -4

A

Step 1

B

Step 2

C

Step 3

D

There is no error

Correct Answer: B

Choice B is the correct answer. Identify where the inequality rule was violated.

  1. Step 1 Check: Subtract 3 from both sides. 3−2x−3≤11−3→−2x≤83 - 2x - 3 \leq 11 - 3 \rightarrow -2x \leq 8. This is correct.
  2. Step 2 Check: Divide by -2. −2x−2≤8−2\frac{-2x}{-2} \leq \frac{8}{-2}. Since we divided by a negative, the sign MUST reverse. It should be x≥−4x \geq -4. The step shows x≤−4x \leq -4, which is incorrect.

?�� Strategic Tip: Always double-check the inequality direction when multiplying or dividing by a negative number.

Choice A is incorrect because Step 1 correctly subtracts 3. Choice C is incorrect because Step 3 is just interpreting Step 2, so the root error is in Step 2. Choice D is incorrect because the sign was not reversed in Step 2.

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Linear Functions Set 69