Question

How do you solve \[12(x+3)-3x=117\]?

Answer 1

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

Complete step by step answer:
As per the given question, we are provided with an equation that is to be simplified to get the solution of the equation. A solution is that which when substituted back into the equation, both the sides of the equation will be equal. Here, the given equation is \[12(x+3)-3x=117\].
In the given equation, we need to simplify \[12(x+3)\]. We need to distribute the monomial outside the parentheses of given polynomials to each term of the polynomial. By splitting up the equation, we can expand \[12(x+3)\] into the following equation:
\[\Rightarrow 12(x)+12(3)\]
We know that, \[12(x)\] is equal to \[12x\]; \[12(3)\] is equal to \[36\]. By substituting all these terms into the previous equation, we get
\[\Rightarrow 12x+36\]
Now, substituting the above value into the left hand side of equation, we get
\[\Rightarrow 12x+36-3x\]
Now, we need to rearrange the terms in the above equation for simplification. So, we get
\[\Rightarrow 12x-3x+36\]
Addition of \[12x\] and \[-3x\] gives \[9x\], then on substitution we get
\[\Rightarrow 9x+36\]
Now substituting the above value in the whole equation, we get
\[\Rightarrow 9x+36=117\]
Now, we have to isolate x by subtracting 36 from both sides of the equation. Then, we get
\[\Rightarrow 9x+36-36=117-36\to 9x+0=81\to 9x=81\]
As we know that the division of 81 by 9 is equal to 9, we can rewrite the equation as
\[\Rightarrow 9x=81\to x=\dfrac{81}{9}\to x=9\]
\[\therefore \] \[x=9\] is the required solution of \[12(x+3)-3x=117\].

Note:
Note: We can rather solve the equation by multiplying 12 with \[x+3\] and adding \[-3x\] to it, then simplifying on the left-hand side to get \[9x+36\]. And shifting 36 to the right hand side to get 81. And dividing 81 with 9, we can get the solution as \[\begin{align}
  & \Rightarrow 12(x+3)-3x=117\Rightarrow 12x+36-3x=117\Rightarrow 9x+36=117 \\
 & \Rightarrow 9x=117-36=81\Rightarrow x=\dfrac{81}{9}=9 \\
\end{align}\].
We should avoid calculation mistakes to get the correct solution.