Question

Given that $f\left( x \right) = 2x - 5$, how do you find the value of x that makes $f\left( x \right) = 15$?

Answer 1

Hint: In this question, we want to solve the linear equation of one variable. A linear equation of one variable can be written in the form $ax + b = c$. Here, a, b, and c are constants. And the exponent on the variable of the linear equation is always 1. To solve the linear equation, we have to remember that addition and subtraction are the inverse operations of each other. For example, if we have a number that is being added that we need to move to the other side of the equation, then we would subtract it from both sides of that equation.

Complete step by step solution:
In this question, we want to find the value of the variable ‘x’.
The given equation is,
$ \Rightarrow f\left( x \right) = 2x - 5$ ...(1)
We want to find the value of x at $f\left( x \right) = 15$.
Substitute the value of f(x) in equation (1).
$ \Rightarrow 15 = 2x – 5$
First, we will add 5 on both sides.
$ \Rightarrow 15 + 5 = 2x - 5 + 5$
Let us apply addition on both sides. The addition of -5 and 5 is equal to 0 on the right-hand side, and the subtraction of 15 and 5 is equal to 20 on the left-hand side.
That is equal to,
$ \Rightarrow 20 = 2x$
Now, let us divide by 2 into both sides.
$ \Rightarrow \dfrac{{20}}{2} = \dfrac{{2x}}{2}$
Let us apply division on both sides. The division of 2x and 2 is equal to x on the right-hand side, and the division of 20 and 2 is equal to 10 on the left-hand side.
Therefore,
$ \Rightarrow x = 10$

Hence, the solution of the given equation is 10.

Note:
Let us verify the answer.
$ \Rightarrow f\left( x \right) = 2x - 5$
Let us substitute the value of x is equal to 10 in the above equation.
$ \Rightarrow f\left( x \right) = 2\left( {10} \right) - 5$
That is equal to,
$ \Rightarrow f\left( x \right) = 20 - 5$
Let us apply subtraction on the left-hand sides.
$ \Rightarrow f\left( x \right) = 15$
Hence, the answer we get is correct.