Question

How do you solve $\dfrac{j}{4}-8<4$?

Answer 1

Hint: In the equation we have an inequality i.e., less than. In the given expression we can observe the two arithmetic operations first one is division and the second one is subtractions. According to the BODMOS rule we will first apply subtraction and second division. To solve the inequality, we need to apply the reverse operations for the given operations. The first operation is subtraction, so we will perform the addition operation on both sides of the expression similarly we will apply the multiplication operation for division operation. Now we will get our required result.

Complete step-by-step answer:
Given that, $\dfrac{j}{4}-8<4$.
In the above expression we have subtracting $8$ on the left side. To solve the above expression, we need to add the same $8$ on both sides. Then we will get
$\dfrac{j}{4}-8+8<4+8$
We know that $+x-x=0$, then we will have
$\dfrac{j}{4}<12$
In the above simplified expression, we can observe that $4$ is dividing $j$ on LHS. To solve the above expression, we will multiply the same $4$ on both sides. Then we will have
$\dfrac{j}{4}\times 4<12\times 4$
We know that $a\times \dfrac{1}{a}=1$, then we will get
$\therefore j < 48$.

Note: We can check whether the obtained result is right or wrong by plugging in any value in the given expression and checking the condition. Let us take the value $50$ as $j$. Then the value of
$\begin{align}
  & \dfrac{j}{4}=\dfrac{50}{4} \\
 & \Rightarrow \dfrac{j}{4}=12.5 \\
\end{align}$
And the value of $\dfrac{j}{4}-8$ is given by
$\begin{align}
  & \dfrac{j}{4}-8=12.5-8 \\
 & \Rightarrow \dfrac{j}{4}-8=4.5>4 \\
\end{align}$
Hence the obtained result is correct.