Question

How do you solve \[7x-5=6x-2\]?

Answer 1

Hint: An equation can be solved by taking all the constants one side and unknowns to the other side of the equation. The constant side must be solved step-by-step to get through the solution. We need to do the addition, subtraction, multiplication and division operations in such a way to simplify the equation.

Complete step by step answer:
As per the given question, we are provided with an equation which is to be simplified to get the solution of the equation. A solution is which when substituted back into the equation, both the sides of the equation will be equal. Here, the given equation is \[7x-5=6x-2\].
Our main goal is to find the value of x. So, first we need to isolate x. In this case, we have to subtract \[6x\] from both the sides of the equation. That is, we can write it as
\[\Rightarrow 7x-5-6x=6x-2-6x\]
In the left-hand side of the above equation, subtraction of \[6x\] from \[7x\] is equal to \[x\] and in the right-hand side of the equation, subtraction \[6x\] from \[6x\] gives zero. Thus, we can rewrite the above equation as
\[\Rightarrow x-5=-2\]
Now, to isolate \[x\], we need to add 5 on both sides of the previous equation. That is, we write it as
\[\Rightarrow x-5+5=-2+5\]
In the left-hand side of the equation, subtraction of 5 from 5 gives 0 and in the right-hand side of the equation, subtraction of 2 from 5 gives 3. Then, we can rewrite the previous equation as
\[\Rightarrow x=3\]
 When we substitute \[x=3\] back into the equation, we get
\[\Rightarrow 7x-5=6x-2\to 7(3)-5=6(3)-2\to 21-5=18-2\to 16=16\].

\[\therefore x=3\] is the solution of the given equation \[7x-5=6x-2\].

Note: We can rather solve the given equation by shifting \[6x\] in the right-hand side to left-hand side, -5 from left-hand side to right-hand side and then subtracting 2 from 5 to get \[x=3\] as the solution. This is a two-step solution which involves just two steps towards the solution. We should avoid calculation mistakes to get the correct solution.