Question

Solve ech of the following question. Also, verify the result in each case.
$0.5x+\frac{x}{3}=0.25x+7$

Answer 1

$$\begin{gathered} 0.5x+\frac{x}{3}=0.25x+7 \\ \Rightarrow \frac{05}{10}\text{x}+\frac{\text{x}}{3}=\frac{25\text{x}}{100}+7 \\ \Rightarrow \frac{x}{2}+\frac{x}{3}=\frac{x}{4}+7 \end{gathered}$$
Transposing x/4 to LHS, we get

$\Rightarrow \frac{x}{2}+\frac{x}{3}-\frac{x}{4}=7$
$$\begin{gathered} \Rightarrow \frac{6x+4x-3x}{12}=7 \\ \Rightarrow \frac{7x}{12}=7 \end{gathered}$$
Multiplying both sides by 12, we get
=> $\frac{7x}{12}\times 12=7\times 12$
=> 7x = 84
Dividing both sides by 7, we get
=> $\frac{7x}{7}=\frac{84}{7}$
=> x = 12
Verification:
Substituting x = 12 on both sides, we get
$0.5\left(12\right)+\frac{12}{3}=0.25\left(12\right)+7$
6 + 4 = 3 + 7
10 = 10
LHS =RHS
Hence, verified.