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# How do you solve for $x$: $\dfrac{12}{x}+\dfrac{3}{4}=\dfrac{3}{2}$?

Last updated date: 09th Aug 2024
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Hint:This is a linear equation in one variable as there is only one variable in an equation. In the given question, the variable is the letter ‘x’, to solve this question we need to get ‘x’ on one side of the “equals” sign, and all the other numbers on the other side. To solve this equation for a given variable ‘x’, we have to undo the mathematical operations such as addition, subtraction, multiplication and division that have been done to the variables.

Complete step by step solution:
We have given that,
$\Rightarrow \dfrac{12}{x}+\dfrac{3}{4}=\dfrac{3}{2}$
Subtracting $\dfrac{3}{4}$ from both the sides of the equation, we get
$\Rightarrow \dfrac{12}{x}+\dfrac{3}{4}-\dfrac{3}{4}=\dfrac{3}{2}-\dfrac{3}{4}$
$\Rightarrow \dfrac{12}{x}=\dfrac{3}{2}-\dfrac{3}{4}$
Taking the LCM of 2 and 4 on the right side of the equation,,
LCM of 2 and 4 is 4
$\Rightarrow \dfrac{12}{x}=\dfrac{3\times 2}{2\times 2}-\dfrac{3}{4}$
$\Rightarrow \dfrac{12}{x}=\dfrac{6}{4}-\dfrac{3}{4}$
$\Rightarrow \dfrac{12}{x}=\dfrac{3}{4}$
Multiplied both the sides by $x$, we get
$\Rightarrow 12=\dfrac{3}{4}x$
Multiplied both the sides of the equation by 4, we get
$\Rightarrow 48=\dfrac{3x}{4}\times 4$
Simplifying the above, we get
$\Rightarrow 48=3x$
Dividing both the sides by, we get
$\Rightarrow x=\dfrac{48}{3}=16$
$\Rightarrow x=16$
Therefore, the value of ‘x’ is equal to 16.
It is the required solution.