Question

25/40
which step should you perform first in the following
equation:
\\(\frac{2}{3}x + 7 = 15\\)
add 7 to both sides
multiply both sides by \\(\frac{3}{2}\\)
subtract 7 from both sides
multiply both sides by \\(\frac{2}{3}\\)

Explanation:

Step1: Recall Order of Operations

To solve $\frac{2}{3}x + 7 = 15$ for $x$, we use inverse operations. The equation has addition (of 7) and multiplication (of $\frac{2}{3}$ with $x$). We reverse operations in the order of PEMDAS (undo addition/subtraction before multiplication/division).

Step2: Analyze Each Option

• "Add 7 to both sides": This would increase the constant term, not isolate $x$, so incorrect.
• "Multiply both sides by $\frac{3}{2}$": This is for undoing the multiplication by $\frac{2}{3}$, but we first need to isolate the term with $x$ (undo the addition of 7), so too early.
• "Subtract 7 from both sides": Subtracting 7 from both sides undoes the $+7$, isolating $\frac{2}{3}x$ (since $\frac{2}{3}x + 7 - 7 = \frac{2}{3}x$ and $15 - 7 = 8$), which is the correct first step.
• "Multiply both sides by $\frac{2}{3}$": This would complicate the equation (e.g., $\frac{2}{3}x \cdot \frac{2}{3} + 7 \cdot \frac{2}{3} = 15 \cdot \frac{2}{3}$), not isolate $x$, so incorrect.

Answer:

Subtract 7 from both sides