Question

How do you solve \[a+3\left( 4a+8 \right)=128\]?

Answer 1

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 ‘\[a\]’, to solve this question we need to get ‘\[a\]’ on one side of the “equals” sign, and all the other numbers on the other side. To solve this equation for a given variable ‘\[a\]’, 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 the given equation,
\[\Rightarrow a+3\left( 4a+8 \right)=128\]
Simplifying the above equation, we get
\[\Rightarrow a+12a+24=128\]
Combining the like terms in the above equation, we get
\[\Rightarrow 13a+24=128\]
Subtract 24 from both the sides of the equation,
\[\Rightarrow 13a+24-24=128-24\]
Simplifying the numbers in the above equation, we get
\[\Rightarrow 13a=104\]
Dividing both the sides of the above equation by 13, we get
\[\Rightarrow a=8\]
Therefore,
The possible value of \[a\] is equal to 8.
It is the required answer.

Additional information: In the given question, no mathematical formula is being used only the mathematical operations such as addition, subtraction, multiplication and division is 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.