Question

fiona solved the equation shown.
\\(\frac{1}{2} - \frac{1}{3}(6x - 3) = -\frac{13}{2}\\)
fionas solution

steps	resulting equations
2: \\(_________\\)	\\(\frac{3}{2} - 2x = -\frac{13}{2}\\)
3: isolate the variable expression by using the addition property of equality.	\\(-2x = -8\\)
4: isolate the variable by using the division property of equality.	\\(x = 4\\)

what is the missing step of her solution?

• simplify by using the addition property of equality.
• simplify by using the multiplication property of equality.
• simplify by combining like terms.
• simplify by using the division property of equality.

Explanation:

Step1: Analyze the first and second equations

In step 1, the equation is $\frac{1}{2}-2x + 1=-\frac{13}{2}$. In step 2, the equation is $\frac{3}{2}-2x=-\frac{13}{2}$. We can see that $\frac{1}{2}+ 1=\frac{1 + 2}{2}=\frac{3}{2}$, which means we combined the constant terms (like terms) $\frac{1}{2}$ and $1$.

Step2: Match with the options

The operation of combining $\frac{1}{2}$ and $1$ is combining like terms. So the missing step is simplifying by combining like terms.

Answer:

Simplify by combining like terms.