Question

How do you solve $2x+6=18$?

Answer 1

Hint: We will verify that the given equation is a linear equation in one variable. We will solve this linear equation in one variable to obtain the solution of the equation. We will shift all the constant terms on one side of the equation. Then we will divide both sides of the equation by the coefficient of the variable. After that, we will get the value of the variable.

Complete step by step answer:
The given equation is $2x+6=18 $. We can see that there is only one variable present in the given equation. The only power of this variable is 1. Hence, the given equation is a linear equation. Now, we have to solve this linear equation in one variable to obtain the solution of this equation. Since it is only one linear equation and it has only one variable, there is only one solution to this equation.
Let us shift the constant terms to one side of the equation. There are two constant terms, 6 and 18, in the given equation. We will shift the term 6 to the right hand side, which does not have any term with the variable. So, we get the following equation,
$2x=18-6$
We know that $18-6=12$. Therefore, we can write the above equation as
$2x=12$
Now, we will divide both sides of the equation by the coefficient of the variable, which is 2. So, we get the following,
\[\begin{align}
  & \dfrac{2x}{2}=\dfrac{12}{2} \\
 & \therefore x=6 \\
\end{align}\]

Therefore, we have obtained $x=6$ as the solution of the given linear equation.

Note: An equation can be classified by looking at the number of variables and the degree of the equation. The degree of the equation is the highest power of the variables in one term. A linear equation is the equation with degree 1. If the equation has degree 2, then it is called a quadratic equation. A cubic equation is the equation with degree 3. Depending on the degree of the equation, the number of values of x can be obtained. So, for linear, x can have 1 value, for quadratic, its 2 and for cubic its 3.