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

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Last updated date: 29th Feb 2024
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IVSAT 2024
Answer
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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.
Additional information:
In the given question, no mathematical formula is being used; only the mathematical operations such as addition, subtraction, multiplication and division are used.
● Use addition or subtraction properties of equality to gather variable terms on one side of the equation and constant on the other side of the equation.
● Use the multiplication or division properties of equality to form the coefficient of the variable term equivalent to 1.

Note: The important thing to recollect about any equation is that the ‘equals’ sign represents a balance. What the sign says is that what’s on the left-hand side is strictly an equal to what’s on the right-hand side. It is the type of question where only mathematical operations such as addition, subtraction, multiplication and division is used.
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