Question

How do you solve \[3\left( 5j+2 \right)=2\left( 3j-6 \right)\]?

Answer 1

Hint: As we can see that the equation has only variables and constants in it, so it is a one-variable equation. The highest power of the variable j in this equation is one, this means that it is a linear equation in one variable. To solve this, we need to take all the terms having the variable j to the left side, and the constant to the right side. Also, to simplify this equation, we have to use the distributive property, the property states the expansion \[a\left( b+c \right)=ab+ac\].

Complete step by step solution:
We are given the equation \[3\left( 5j+2 \right)=2\left( 3j-6 \right)\], 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.
\[3\left( 5j+2 \right)=2\left( 3j-6 \right)\]
Simplifying the above expression using the distributive property, we get
\[\Rightarrow 15j+6=6j-12\]
Subtracting \[6j\] from both sides of above expression, we get
\[\begin{align}
  & \Rightarrow 9j+6=-12 \\
 & \Rightarrow 9j=-12-6=-18 \\
\end{align}\]
Dividing both sides of the above equation by 9, we get
\[\therefore j=-2\]
Hence, the solution of the given equation is \[j=-2\].

Note: We can check if the solution is correct or not by substituting the value we got in the equation. For the given equation, the left-hand side is \[3\left( 5j+2 \right)\], and the right-hand side is \[2\left( 3j-6 \right)\]. Substituting \[j=-2\] in both sides of the above equation, we get LHS as \[3\left( 5(-2)+2 \right)=3\left( -8 \right)=-24\], and \[RHS=2\left( 3(-2)-6 \right)=2(-12)=-24\]. As \[LHS=RHS\] the solution is correct.