Question

How do you solve \[3\left( 5x-1 \right)=3x+3\]?

Answer 1

Hint: To solve the given equation we first need to simplify it by expanding the term \[3\left( 5x-1 \right)\]. We can do this by using the distributive property, the property states the expansion \[a\left( b+c \right)=ab+ac\]. This is a linear equation in one variable as the only variable it has is x. After expanding it as, to solve this equation, we need to take the variable terms to one side and the constant terms to the other side of the equation. By doing this, we can find the solution value for the given equation.

Complete step by step solution:
We are given the equation \[3\left( 5x-1 \right)=3x+3\], we have to solve it. The highest power of the variable of the equation is 1, so the degree of the equation is also one. Hence, it is a linear equation. As we know to solve a linear equation, we have to take all the variable terms to one side of the equation and leave constants to the other side.
\[3\left( 5x-1 \right)=3x+3\]
Simplifying the above expression using the distributive property, we get
\[\Rightarrow 15x-3=3x+3\]
Subtracting \[3x\] from both sides of the above expression, we get
\[\begin{align}
  & \Rightarrow 12x-3=3 \\
 & \Rightarrow 12x=3+3=6 \\
\end{align}\]
Dividing both sides of the above equation by 12, we get
\[\therefore x=\dfrac{1}{2}\]
Hence, the solution of the given equation is \[x=\dfrac{1}{2}\].

Note: We can also solve the given equation without using distributive property as follows,
\[3\left( 5x-1 \right)=3x+3\]
Dividing both sides of the above equation by 3, we get
\[\begin{align}
  & \Rightarrow \dfrac{3\left( 5x-1 \right)}{3}=\dfrac{3x+3}{3} \\
 & \Rightarrow 5x-1=x+1 \\
\end{align}\]
Subtracting x from both sides of the above equation, we get
\[\begin{align}
  & \Rightarrow 4x-1=1 \\
 & \Rightarrow 4x=2 \\
 & \therefore x=\dfrac{1}{2} \\
\end{align}\]
Thus, we are getting the same answer from both methods.