Question

How do you solve $2\left( 3x-6 \right)=3\left( 2x-4 \right)$?

Answer 1

Hint: There are two multiplications on both sides of the equality. We first multiply the constants with the terms under parenthesis. We take all the variables and the constants into consideration. Then using the equality of the equation, we get an infinite number of solutions for the equation $2\left( 3x-6 \right)=3\left( 2x-4 \right)$.

Complete step by step solution:
The given equation $2\left( 3x-6 \right)=3\left( 2x-4 \right)$ is a linear equation of x. We need to simplify the equation by completing the multiplication of the constants separately.
All the terms in the equation of $2\left( 3x-6 \right)=3\left( 2x-4 \right)$ are either variables of x or a constant. We break the multiplication by multiplying 2 with $\left( 3x-6 \right)$ and 3 with $\left( 2x-4 \right)$.
So, $2\left( 3x-6 \right)=6x-12$ and $3\left( 2x-4 \right)=6x-12$.
The equation becomes $6x-12=6x-12$.
We can see that the equations on both sides are equal which will not give any particular solution for x.
Any value of x will make the equation on both sides equal to each other.
Therefore, there are an infinite number of solutions for the equation $2\left( 3x-6 \right)=3\left( 2x-4 \right)$.

Note: To confirm the result of the solution being $x=a$, $a$ being any arbitrary value of x for equation $2\left( 3x-6 \right)=3\left( 2x-4 \right)$, we put the value on both sides of the equation and find the final value.
Therefore, the left-hand side of the equation becomes \[2\left( 3x-6 \right)=2\left( 3a-6 \right)=6a-12\].
The right-hand side of the equation becomes \[3\left( 2x-4 \right)=3\left( 2a-4 \right)=6a-12\]
Thus, verified for the equation $2\left( 3x-6 \right)=3\left( 2x-4 \right)$ the number of solutions is infinite.