Question

How do you solve $3\left( 4x+5 \right)=12$?

Answer 1

Hint: We separate the variables and the constants of the equation $3\left( 4x+5 \right)=12$ after completing the multiplication. We apply the binary operation of addition and subtraction for both variables and constants. The solutions of the variables and the constants will be added at the end to get the final answer to equate with 0. Then we solve the linear equation to find the value of $x$.

Complete step by step solution:
We complete the single multiplication in the equation of $3\left( 4x+5 \right)=12$.
Multiplying 3 with $\left( 4x+5 \right)$, we get $3\left( 4x+5 \right)=12x+15$.
The equation becomes $12x+15=12$
The given equation $12x+15=12$ is a linear equation of $x$. We need to simplify the equation by solving the variables and the constants separately.
All the terms in the equation of $12x+15=12$ are either variable of $x$ or a constant. We first separate the variables.
We take the constants all together to solve it.
$\begin{align}
  & 12x+15=12 \\
 & \Rightarrow 12x=12-15 \\
\end{align}$
There are two such constants which are 12 and 15.
Now we apply the binary operation of subtraction to get
$\Rightarrow 12x=12-15=-3$.
The binary operation between them is addition which gives us $12x=-3$.
Now we divide both sides of the equation with 12 to get
\[\begin{align}
  & 12x=-3 \\
 & \Rightarrow \dfrac{12x}{12}=\dfrac{-3}{12} \\
 & \Rightarrow x=-\dfrac{1}{4} \\
\end{align}\]
Therefore, the final solution becomes \[x=-\dfrac{1}{4}\].

Note: We can also solve the equation starting it with the division.
Therefore, we divide both sides of $3\left( 4x+5 \right)=12$ by 3 and get
$\begin{align}
  & \dfrac{3\left( 4x+5 \right)}{3}=\dfrac{12}{3} \\
 & \Rightarrow 4x+5=4 \\
\end{align}$
We take the constants together.
$4x=4-5=-1$ which gives \[x=-\dfrac{1}{4}\]
The solution is \[x=-\dfrac{1}{4}\].