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How do you solve for\[x\]: \[3-x=12\left( x-1 \right)\]?

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Last updated date: 13th Jun 2024
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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. For example- in the given equation we have 3-x on the left-hand side, we can easily see that a number 3 is added to ‘x’, so we undo this step by subtraction 3 from the whole equation and this manner we get the solution of the question.

Complete step by step solution:
We have the given equation;
\[\Rightarrow 3-x=12\left( x-1 \right)\]
Subtract 3 from both the sides of the equation,
\[\Rightarrow 3-x-3=12\left( x-1 \right)-3\]
Simplify, subtract the numbers
\[\Rightarrow -x=12\left( x-1 \right)-3\]
Simplifying the right hand side of the equation, we get
\[\Rightarrow -x=12x-12-3\]
Simplifying the numbers, we get
\[\Rightarrow -x=12x-15\]
Subtract 12x from both the sides of the equation, we get
\[\Rightarrow -x-12x=12x-15-12x\]
Combining the like terms, we get
\[\Rightarrow -13x=-15\]
Dividing both the sides of the equation by 13, we get
\[\Rightarrow -x=-\dfrac{15}{13}\]
Cancelling out the negative sign, we get
\[\Rightarrow x=\dfrac{15}{13}\]
Therefore, the value of ‘x’ is equal to \[\dfrac{15}{13}\].
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.