Question

How do you solve \[-3\left( 6+3x \right)=-72\]?

Answer 1

Hint: We will use the distributive property to simplify the equation, the distributive property is \[a\left( b+c \right)=ab+ac\]. The degree of an equation is the highest power to which the variable in the equation is raised. If the degree of the equation is one, then it is a linear equation. 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. By this, we can find the solution value of the equation.

Complete step by step solution:
We are given the equation \[-3\left( 6+3x \right)=-72\], 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.
\[-3\left( 6+3x \right)=-72\]
Using the distributive property, we can expand the bracket on the LHS to simplify above equation, by using this property we get
\[\Rightarrow -18-9x=-72\]
Adding 18 to both sides of above equation, we get
\[\Rightarrow -9x=-72+18=-54\]
Dividing both sides of above equation by \[-9\], we get
\[\begin{align}
  & \Rightarrow \dfrac{-9x}{-9}=\dfrac{-54}{-9} \\
 & \therefore x=6 \\
\end{align}\]
Hence, the solution of the given equation is \[x=6\].

Note: We can also solve the problem without using the distributive property as follows,
The given equation is \[-3\left( 6+3x \right)=-72\]. Dividing by \[-3\] to both sides of the above equation, we get
\[\begin{align}
  & \Rightarrow \dfrac{-3\left( 6+3x \right)}{-3}=\dfrac{-72}{-3} \\
 & \Rightarrow 6+3x=24 \\
\end{align}\]
Subtracting 6 from both sides, we get
\[\Rightarrow 3x=24-6=18\]
\[\therefore x=6\]
Thus, we get the same answer from both methods.