Question

Six times the sum of a number and 3 is 12 less than the 12 times the number. How do you find the number?

Answer 1

Hint: In the given question, we have been asked to find the value of ‘x’. We need to first change the statement into a mathematical equation and 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,
Six times the sum of a number and 3 is 12 less than the 12 times the number.
Let the number be ‘x’.
Now converting the given statement into mathematical equation, we get
\[\Rightarrow 6\left( x+3 \right)=12x-12\]
Now, solving for the value of ‘x’.
Simplifying the above equation, we get
\[\Rightarrow 6x+18=12x-12\]
Subtracting 18 from both the sides of the equation, we get
\[\Rightarrow 6x+18-18=12x-12-18\]
Simplifying the numbers, we get
\[\Rightarrow 6x=12x-30\]
Subtracting 12x from both the sides of the equation, we get
\[\Rightarrow 6x-12x=12x-30-12x\]
Combining the like terms, we get
\[\Rightarrow -6x=-30\]
Cancelling out the negative sign, we get
\[\Rightarrow 6x=30\]
Dividing 6 from both the sides of the equation, we get
\[\Rightarrow x=5\]

Therefore, x is equals to 5 is the required answer.

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.