Question

Given $h\left( x \right) = 4x - 5$, how do you solve for x when $h\left( x \right) = - 1$?

Answer 1

Hint: In this question, we want to find the value of x when the function value is -1. A linear equation
of one variable can be written in the form $ax + b$. Here, a, and b 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 x.
The given equation is,
$ \Rightarrow h\left( x \right) = 4x - 5$
Let us solve this equation, substitute the value of the given function.
Here, we want to find the value of x when the function value is -1.
So, substitute the value of h(x) is equal to -1.
$ \Rightarrow - 1 = 4x - 5$
Now, let us add 5 on both sides.
$ \Rightarrow - 1 + 5 = 4x - 5 + 5$
Let us simplify the above equation. On the left-hand side, the addition of -1 and 5 is 4. And on the right-hand side the addition of -5 and 5 is 0.
Therefore,
$ \Rightarrow 4 = 4x$
Let us divide both sides by 4.
$ \Rightarrow \dfrac{4}{4} = \dfrac{{4x}}{4}$
The answer is,
$ \Rightarrow x = 1$

Hence, the value of x is 1.

Note: Let us verify the answer by substituting the value of x is equal to 1.
$ \Rightarrow h\left( x \right) = 4x - 5$
Let us substitute the value of x is equal to 1 in the above equation.
$ \Rightarrow h\left( x \right) = 4\left( 1 \right) - 5$
That is equal to,
$ \Rightarrow h\left( x \right) = 4 - 5$
Let us simplify the right-hand side.
$ \Rightarrow h\left( x \right) = - 1$
Hence, the answer we get is correct.