Question

How do you solve $3\left( x-1 \right)=x$ ?

Answer 1

Hint: To solve the given first-degree equation we need to use the four fundamental operations on arithmetic which are addition, subtraction, multiplication, and division, to get the value of the variable, which is also known as the solution of the equation.

Complete step by step answer:
While solving the first-degree equation, we don’t need to apply the operations in a specific order. We need to use the method below to get the solution of the given equation-
First, let’s expand the equation by opening the parentheses or brackets in the L.H.S. and multiply 3 to the terms within the brackets according to the distributive property.
$\Rightarrow 3x-3=x$
Now we will add ‘3’ on both the sides, we get
$\Rightarrow 3x-3+3=x+3$
$\Rightarrow 3x=x+3$
Step3- Now, we need to subtract ‘x’ from both sides of the equation to get the similar terms on either side of the “equal to” sign, i.e. variable terms (x) on L.H.S. and constants on R.H.S.
$3x-x=x+3-x$
$\Rightarrow 2x=3$
Step 4- Now, we will use the division property to make the coefficient of the variable (x) 1. For this, we need to divide both sides of the equation by 2, so that the coefficient of ‘x’ becomes 1. Thus, giving us the solution of the first-degree equation given in the question.
$\Rightarrow \dfrac{2x}{2}=\dfrac{3}{2}$
$\Rightarrow x=\dfrac{3}{2}$
Therefore, the solution of the first-degree equation $3\left( x-1 \right)=x$ is $x=\dfrac{3}{2}$

Note:
Remember to multiply all the terms inside the parentheses with the term outside them, according to the distributive property.
Also, while using arithmetic operations on a term in an equation, make sure to do it on both sides of the equal to sign.