Question

How do you solve \[12+5x=12x-10\] ?

Answer 1

Hint: We will solve this question using basic linear equation concepts. First we have to group like terms as x containing terms on one side and other terms on other sides. Then we have to apply basic arithmetic operations to solve for the value x. By simplifying the equation we got we will arrive at the solution.

Complete step by step solution:
Given equation
\[12+5x=12x-10\]
First we have to group the like terms.
Group the x containing terms on one side and the remaining terms on other sides.
To group the terms we have to subtract 5x from both sides of the equation.
By subtracting 5x we will get
\[\Rightarrow 12+5x-5x=12x-5x-10\]
By simplifying above equation we get
\[\Rightarrow 12=7x-10\]
For further grouping we will add 10 on both sides of the equation.
By adding 10 we will get
 \[\Rightarrow 12+10=7x-10+10\]
By simplifying we will get
\[\Rightarrow 22=7x\]
We have to solve for x. we have to solve for x so we have to rewrite the equation.
By rewriting we will get
\[\Rightarrow 7x=22\]
Now to get the value of x we have to divide with 7 on both sides of the equation.
By dividing we will get
\[\Rightarrow \dfrac{7x}{7}=\dfrac{22}{7}\]
By simplifying we will get the value of x as
\[\Rightarrow x=3.142\]
So by solving the above given equation we will get \[x=3.142\]

Note: We can verify the solution by back substituting the value. substitute the x value in the equation and check whether the LHS and RHS are equal or not. We can solve this question in many simplification ways but above discussed will contain only basic operations to perform.