Question

rahul solved the equation $2\left(x - \frac{1}{8}\
ight) - \frac{3}{5}x = \frac{55}{4}$. in which step did he use the addition property of equality?
rahul’s solution

steps	resulting equations
2	$\frac{7}{5}x - \frac{1}{4} = \frac{55}{4}$
3	$\frac{7}{5}x = \frac{56}{4}$
4	$x = 10$

\\(\bigcirc\\) step 1
\\(\bigcirc\\) step 2

Explanation:

Step1: Recall addition property of equality

The addition property of equality states that if you add the same value to both sides of an equation, the equality still holds.

Step2: Analyze Step 1

Step 1 expands $2(x-\frac{1}{8})$ to get $2x-\frac{1}{4}-\frac{3}{5}x=\frac{55}{4}$. This uses the distributive property, not the addition property.

Step3: Analyze Step 2

Step 2 combines like terms $2x-\frac{3}{5}x$ to get $\frac{7}{5}x-\frac{1}{4}=\frac{55}{4}$. This is combining like terms, not the addition property.

Step4: Analyze Step 3

Step 3 transforms $\frac{7}{5}x-\frac{1}{4}=\frac{55}{4}$ to $\frac{7}{5}x=\frac{56}{4}$. This is done by adding $\frac{1}{4}$ to both sides of the equation, which uses the addition property of equality.

Step5: Analyze Step 4

Step 4 solves for $x$ by multiplying both sides by $\frac{5}{7}$, which uses the multiplication property of equality.

Answer:

Step 3