Question

How do you solve 4x-2=2x+8?

Answer 1

Hint: In this type of question, we will arrange the equation by making the equation in the standard form of ax+b=0. We will take all the variables (or we can say x) to the left side of the equation and all the constants to the right side of the equation. We will balance the equation. So, we can solve the given equation to get the value of x.

Complete step by step answer:
Let us solve the question.
The given equation which we have to solve is
4x-2=2x+8
We know that the standard form of the linear equation is always of degree 1.
We can say that ax+b=0 is a form of the linear equation where a is not equal to zero.
Let us make the equation 4x-2=2x+8 in the standard form.
We will put all the terms of x on the left side of the equation and all the constant terms on the left side of the equation.
First, let us balance the equation.
4x-2+2=2x+8+2
\[\Rightarrow \]4x+0=2x+10
\[\Rightarrow \]4x-2x=2x-2x+10
\[\Rightarrow \]2x=0+10
\[\Rightarrow \]2x=10
Now, we divide the number 10 by the number 2 to get the value of x.
\[\Rightarrow x=\dfrac{10}{2}=5\]
Hence, we get the value of x as 5.

Note:
The first-degree equation that we have taken in this question always has only one solution. The solutions of such equations can be found easily. There is an alternate method to solve this.
We can solve this question using an additional subtraction property.
4x-2=2x+8
\[\Rightarrow \]4x=2x+8+2
\[\Rightarrow \]4x=2x+10
\[\Rightarrow \]4x-2x=10
\[\Rightarrow \]2x=10
Now, we divide 10 by 2, so we get x.
\[\Rightarrow x=\dfrac{10}{2}=5\]
Hence, we got the same value using the alternate method. So, we can also use the addition subtraction method to solve this type of question.