Question

Solve the following equations and check the solutions obtained.

$\frac{9x}{2}-4=14$

Answer 1

Step 1: Solve the equation

We have, $\frac{9x}{2}-4=14$

Adding $4$to both sides,

$$\begin{gathered} \frac{9x}{2}-4+4=14+4 \\ \Rightarrow \frac{9x}{2}-0=18 \\ \Rightarrow \frac{9x}{2}=18 \end{gathered}$$

Multiplying both sides by $\frac{2}{9}$

$$\begin{gathered} \frac{9x}{2}\times \frac{2}{9}=18\times \frac{2}{9} \\ \Rightarrow x=4 \end{gathered}$$

Hence, $x=4$ is the solution of the given equation.

Step 2: Check the solution

Given equation is $\frac{9x}{2}-4=14$

At, $x=4$

$$\begin{gathered} L.H.S.=\frac{9x}{2}-4 \\ =\frac{9}{2}\times 4-4 \\ =18-4 \\ =14 \end{gathered}$$

and, $R.H.S.=14$

Clearly, $L.H.S.=R.H.S.$

Hence, $x=4$ is the solution of the given equation.