Question

How do you solve \[9x-8+4x=7x+16\]?

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 ‘\[x\]’, 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 the given equation,
\[\Rightarrow 9x-8+4x=7x+16\]
Combining the like terms in the above equation, we get
\[\Rightarrow 13x-8=7x+16\]
Adding 8 to both the sides of the equation,
\[\Rightarrow 13x-8+8=7x+16+8\]
Simplifying the numbers in the above equation, we get
\[\Rightarrow 13x=7x+24\]
Subtracting 7x from both the side of the equation, we get
\[\Rightarrow 13x-7x=7x+24-7x\]
Combining the like terms in the above equation, we get
\[\Rightarrow 6x=24\]
Dividing both the side of the equation by 6, we get
\[\Rightarrow x=4\]
Therefore,
The possible value of \[x\] is equal to 4.
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.
i) 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.
ii) 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.