Question

1.1 study: solving multistep linear equations

what is the second step?
hint: a fraction multiplied by its reciprocal is equal to 1.

a. multiply both sides by \\(\frac{3}{2}\\)
b. multiply both sides by \\(\frac{2}{3}\\)
c. add \\(\frac{2}{3}x\\) to both sides
d. subtract 4 from both sides.

the second step is:
choice a
choice b
choice c
choice d

Explanation:

Analyze the context and hint

The problem asks for the second step in solving a multistep linear equation. The hint states: "A fraction multiplied by its reciprocal is equal to 1."

Evaluate the options based on the hint

The hint specifically points to multiplying by a reciprocal to isolate a variable or simplify a fractional coefficient.

• Option A: Multiply both sides by \(\frac{3}{2}\).
• Option B: Multiply both sides by \(\frac{2}{3}\).

The reciprocal of \(\frac{2}{3}\) is \(\frac{3}{2}\). Multiplying by the reciprocal \(\frac{3}{2}\) would result in \(1\). Therefore, Option A is the correct step described by the hint.

Match with the multiple-choice selection

The correct choice is Choice A.

Answer:

• Choice A (Correct answer)
• Choice B
• Choice C
• Choice D