Question

Solve for the value of ‘x’ if: $\dfrac{15}{4}-7x=9$.

Answer 1

We have been given linear equations in one variable and we need to find a solution to this equation. We will use the collection method to solve our problem. In this method, all the variable terms are written on one side of the equation whereas all the constant terms are written on another side of the equation. This gives us an equation in a single variable, thus giving us a solution. We shall proceed like this to get our answer.

Complete step by step solution:
The linear equation given to us in the problem is equal to:
$\Rightarrow \dfrac{15}{4}-7x=9$
In the above expression, let us first of all rewrite all the fractional terms in their whole number form. This can be done by multiplying each number in our expression by the highest denominator term. This will make the calculations easier to analyze and solve.
In our expression, the highest denominator term is 4. Therefore, we will multiply our expression by 4 on both the sides. This is done as follows:
$\Rightarrow \left( \dfrac{15}{4}-7x \right)\times 4=\left( 9 \right)\times 4$
On simplifying the fractions into their whole number terms, we get the resulting expression as:
$\Rightarrow 15-28x=36$
Now, we can proceed in solving our equation by collecting all the variable terms in the left-hand side of our equation and all the constant terms on the right-hand side of our expression. On doing so, we get:
$\begin{aligned} & \Rightarrow 28x=15-36 \\\ & \Rightarrow 28x=-21 \\\ & \Rightarrow x=-\dfrac{21}{28} \\\ & \therefore x=-\dfrac{3}{4} \\\ \end{aligned}$
Hence, on solving the linear equation $\dfrac{15}{4}-7x=9$, we get the unique result in ‘x’ as $-\dfrac{3}{4}$ . Hence, $x=-\dfrac{3}{4}$ is the solution of our problem.

Note: Whenever solving a problem containing linear equations, we should always verify our answer by putting the solution in the original expression. Here, if we put $x=-\dfrac{3}{4}$, in our original expression, then we get the left-hand value of our expression as: $\dfrac{15}{4}-7\left( -\dfrac{3}{4} \right)=\dfrac{36}{4}$ which is equal to 9. And the right-hand value of our expression is already 9. So, our solution has been verified.