Question

Consider an equation,
$\frac{24x}{y}-5=31x-\frac{5}{y}$
Which of the following step(s) is/are valid?

• A. $\frac{24x}{y}+\frac{5}{y}=5+31x$
• B. $\frac{24x}{y}+\frac{5}{y}-5=31x$
• C. $-31x+\frac{24x}{y}=5+\frac{5}{y}$
• D. $\frac{24x}{y}-5-31x+\frac{5}{y}=0$

Answer 1

Answer: (A), (B), (D)

The correct options are
A $\frac{24x}{y}+\frac{5}{y}=5+31x$
B $\frac{24x}{y}+\frac{5}{y}-5=31x$
D $\frac{24x}{y}-5-31x+\frac{5}{y}=0$

The given equation is $\frac{24x}{y}-5=31x-\frac{5}{y}$

1. Transposing $-5$ from LHS to RHS and transposing $-\frac{5}{y}$ from RHS to LHS we get
$\frac{24x}{y}+\frac{5}{y}=5+31x$.

2. Transposing $-\frac{5}{y}$ from RHS to LHS we get
$\frac{24x}{y}+\frac{5}{y}-5=31x$.

3. Transposing $31x$ and $-\frac{5}{y}$ from RHS to LHS we get
$\frac{24x}{y}-5-31x+\frac{5}{y}=0$.

$\therefore$ Any of the above three steps can be used as the first step to solve the given equation.