Sure, let's analyze Rahul's solution step by step to find out where he used the addition property of equality.
1. Original Equation:
[tex]\[
2\left(x-\frac{1}{8}\right)-\frac{3}{5} x=\frac{55}{4}
\][/tex]
Expanding the first term:
[tex]\[
2x - 2\left(\frac{1}{8}\right) - \frac{3}{5} x=\frac{55}{4}
\][/tex]
Simplifying:
[tex]\[
2x - \frac{1}{4} - \frac{3}{5} x=\frac{55}{4}
\][/tex]
2. Combining Like Terms:
[tex]\[
2x - \frac{3}{5} x - \frac{1}{4}=\frac{55}{4}
\][/tex]
Finding a common denominator for the terms involving [tex]\( x \)[/tex]:
[tex]\[
2x = \frac{10}{5}x \implies \frac{10}{5}x - \frac{3}{5}x = \left(\frac{10-3}{5}\right)x = \frac{7}{5}x
\][/tex]
Thus, we have:
[tex]\[
\frac{7}{5} x - \frac{1}{4}=\frac{55}{4}
\][/tex]
3. Using the Addition Property of Equality:
To isolate the term with [tex]\( x \)[/tex], we add [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]
Simplifying:
[tex]\[
\frac{7}{5} x = \frac{55 + 1}{4} = \frac{56}{4}
\][/tex]
4. Solving for [tex]\( x \)[/tex]:
[tex]\[
\frac{7}{5} x = \frac{56}{4} \implies x = \left(\frac{5}{7}\right) \left(\frac{56}{4}\right)
\][/tex]
Simplifying further:
[tex]\[
x = \frac{5}{7} \times 14 = 10
\][/tex]
Therefore, Rahul used the addition property of equality in Step 3.
