To determine the step at which Rahul used the addition property of equality, let’s carefully examine each step of the solution in detail:
### Initial Equation
The original equation is:
[tex]\[ 2\left(x - \frac{1}{8}\right) - \frac{3}{5}x = \frac{55}{4} \][/tex]
### Step 1
In Step 1, Rahul expands and simplifies the expression:
[tex]\[ 2\left(x - \frac{1}{8}\right) - \frac{3}{5}x = \frac{55}{4} \][/tex]
Expanding:
[tex]\[ 2x - \frac{2}{8} - \frac{3}{5}x = \frac{55}{4} \][/tex]
Simplifying [tex]\(\frac{2}{8}\)[/tex] to [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[ 2x - \frac{1}{4} - \frac{3}{5}x = \frac{55}{4} \][/tex]
### Step 2
Next, in Step 2, Rahul combines like terms:
[tex]\[ 2x - \frac{3}{5}x - \frac{1}{4} = \frac{55}{4} \][/tex]
Converting [tex]\(2x\)[/tex] to [tex]\(\frac{10}{5}x\)[/tex]:
[tex]\[ \frac{10}{5}x - \frac{3}{5}x - \frac{1}{4} = \frac{55}{4} \][/tex]
Combining [tex]\(\frac{10}{5}x\)[/tex] and [tex]\(\frac{3}{5}x\)[/tex]:
[tex]\[ \frac{7}{5}x - \frac{1}{4} = \frac{55}{4} \][/tex]
### Step 3
In Step 3, Rahul isolates the term with [tex]\(x\)[/tex] by adding [tex]\(\frac{1}{4}\)[/tex] to both sides of the equation:
[tex]\[ \frac{7}{5}x - \frac{1}{4} + \frac{1}{4} = \frac{55}{4} + \frac{1}{4} \][/tex]
This simplifies to:
[tex]\[ \frac{7}{5}x = \frac{56}{4} \][/tex]
In this step, Rahul used the addition property of equality. This property states that adding the same number to both sides of an equation helps to isolate the variable without changing the equality.
### Step 4
Finally, in Step 4, Rahul solves for [tex]\(x\)[/tex]:
[tex]\[ \frac{7}{5}x = \frac{56}{4} \][/tex]
Simplifying [tex]\(\frac{56}{4}\)[/tex] to [tex]\(14\)[/tex]:
[tex]\[ \frac{7}{5}x = 14 \][/tex]
Multiplying both sides by [tex]\(\frac{5}{7}\)[/tex]:
[tex]\[ x = 10 \][/tex]
### Conclusion
The addition property of equality was used in Step 3 when Rahul added [tex]\(\frac{1}{4}\)[/tex] to both sides of the equation.
