Question

How do you solve \[4x - 12 = 2(2x - 6)\]?

Answer 1

Hint: According to the above question, we will first try to rearrange all the terms keeping the variable \[x\]as priority. Rearranging the terms makes the equation very easy to solve. After that we can shift all the terms and make the equation equal to zero. By putting all the terms on one side and making it equal to 0 will make it easy to solve.

Complete step-by-step solution:
According to the question, the equation is:
\[4x - 12 = 2(2x - 6)\]
When we try to rewrite the equation, we get:
\[ \Rightarrow 4x - 12 = 4x - 12\]
As you can see, when we are solving the equation, both the terms on opposite sides are equal. So, when we shift all the terms to one side and make it equal to 0, then all the terms will cancel each other.
\[ \Rightarrow 4x - 12 - 4x + 12 = 0\]
 Now, when we solve the equation, we get:
\[ \Rightarrow 0 = 0\]
There is no value for the variable \[x\]. From this answer we can say that the equation has an infinite number of solutions.

Additional information: By solving, we found the result, \[ \Rightarrow 4x - 12 = 4x - 12\], and this shows that both the sides are equal. When both sides are equal in a problem, then the problem is having an infinite number of solutions and the problem is an identity and all the real numbers are its solutions.

Note: The above method is very easy to solve, but there is also a method to solve it. We can add or subtract the same terms respectively which are on either side, so that the terms get canceled out, and we are finally left with the main terms which are mainly the \[x\]terms which we want to solve. Like in the equation \[ \Rightarrow 4x - 12 = 4x - 12\], we can add \[12\] from both sides so that it gets canceled.