Question

How do you solve $96 = 3\left( {4x + 8} \right)$?

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 solve the linear equation of one variable.
The given equation is,
$ \Rightarrow 96 = 3\left( {4x + 8} \right)$
Let us solve this equation,
First, we will divide both sides by 3.
$ \Rightarrow \dfrac{{96}}{3} = \dfrac{{3\left( {4x + 8} \right)}}{3}$
The division of 96 and 3 is 32 on the left-hand side. And the division of 3 and 3 is 1 on the right-hand side.
Therefore,
$ \Rightarrow 32 = 4x + 8$
Now, let us subtract 8 on both sides.
$ \Rightarrow 32 - 8 = 4x + 8 - 8$
The subtraction of 32 and 8 is 24 on the left-hand side. And the subtraction of 8 and 8 is 0 on the right-hand side.
Therefore,
$ \Rightarrow 24 = 4x$
Let us divide both sides by 4.
$ \Rightarrow \dfrac{{24}}{4} = \dfrac{{4x}}{4}$
 The division of 24 and 4 is 6 on the left-hand side. And the division of 4 and 4 is 1 on the right-hand side.
Therefore,
$ \Rightarrow 6 = x$
We can write the above equation as,
$ \Rightarrow x = 6$

Hence, the solution of the given equation is $6$.

Note: Let us verify the answer.
$ \Rightarrow 96 = 3\left( {4x + 8} \right)$
Let us substitute the value of x is equal to 6 in the above equation.
$ \Rightarrow 96 = 3\left( {4\left( 6 \right) + 8} \right)$
That is equal to,
$ \Rightarrow 96 = 3\left( {24 + 8} \right)$
$ \Rightarrow 96 = 3\left( {32} \right)$
Let us apply multiplication on the right-hand side.
$ \Rightarrow 96 = 96$
Hence, the answer we get is correct.