Question

Solve the equation. Check your solution.

$\frac{2}{7}k-\frac{3}{8}=-\frac{19}{8}$

Answer 1

Step 1 : Solve the equation

$\Rightarrow \frac{2}{7}k-\frac{3}{8}=-\frac{19}{8}$

$\Rightarrow \frac{2}{7}k–\frac{3}{8}+\frac{3}{8}=-\frac{19}{8}+\frac{3}{8}$ [ Add $\frac{3}{8}$ to both sides ]

$\Rightarrow \frac{2}{7}k=\frac{-19+3}{8}$

$\Rightarrow \frac{2}{7}k=\frac{-16}{8}$

$\Rightarrow \frac{2}{7}k=-2$

$\Rightarrow \frac{2}{7}k\times \frac{7}{2}=-2\times \frac{7}{2}$ [ Multiply both sides by $\frac{7}{2}$ ]

$\therefore k=-7$

Step 2 : Checking the solution

Check the solution by putting $k=-7$ in the given inequality

We have, $\frac{2}{7}k-\frac{3}{8}=-\frac{19}{8}$

$\Rightarrow \frac{2}{7}\times -7–\frac{3}{8}=-\frac{19}{8}$

$$\begin{gathered} \Rightarrow -2–\frac{3}{8}=-\frac{19}{8} \\ \Rightarrow \frac{(-2\times 8)-3}{8}=-\frac{19}{8} \\ \Rightarrow \frac{-16-3}{8}=-\frac{19}{8} \\ \Rightarrow -\frac{19}{8}=-\frac{19}{8} \\ \Rightarrow \mathrm{LHS}=\mathrm{RHS} \end{gathered}$$

Hence, the required solution is $k=-7$