Question

How do you solve $\dfrac{3}{4}q - 7 = 8$ ?

Answer 1

Hint: In order to solve this question, we are required to take the term with variable $q$ on one side of the equation and the remaining terms on the other side of the equation. Next, we will try to make the coefficient of $q$ equal to $1$ by dividing or multiplying both the sides of the equation by the coefficient of $q$ and therefore, we can find the value of $q$.

Complete step by step answer:
Here in this question, we are given $\dfrac{3}{4}q - 7 = 8$. Let us start solving the question by adding $7$ on each side of the equation. This will isolate the $q$ term and moreover, keep the equation balanced.
$\dfrac{3}{4}q - 7 + 7 = 8 + 7 \\
\Rightarrow \dfrac{3}{4}q - 0 = 15 \\
\Rightarrow \dfrac{3}{4}q = 15 \\ $
Now, we multiply both left-hand and right-hand side of the equation by$\dfrac{4}{3}$to solve for the value of$q$while keeping the equation balanced.
$\dfrac{4}{3} \times \dfrac{3}{4}q = \dfrac{4}{3} \times 15 \\
\Rightarrow q = 4 \times 5 \\
\therefore q = 20 \\ $
Hence, the value of $q$ in equation $\dfrac{3}{4}q - 7 = 8$ is $20$.

Note:The given question was an easy one and can be easily solved by using the basic knowledge of arithmetic operations. The only possible mistake which students are likely to make in such types of questions are calculation mistakes. So, they should solve such questions very carefully. Now that we know the value of $q$ is $20$, there is a way to double check our answer. In order to double check the solution we are supposed to substitute the value of $q$ which we got as $20$ in the given equation, $\dfrac{3}{4}q - 7 = 8$.
$\dfrac{3}{4}q - 7 = 8 \\
\Rightarrow \dfrac{3}{4}\left( {20} \right) - 7 = 8 \\
\Rightarrow 3 \times 5 - 7 = 8 \\
\Rightarrow 15 - 7 = 8 \\
\Rightarrow 8 = 8$
Now, the left-hand side is equal to the right-hand side. So, we can conclude that our solution or the value of $q$ which we calculated was correct.