Question

How do you solve $\dfrac{3}{4}\left( x+2 \right)=-1$?

Answer 1

Hint: We multiply both sides of the equation $\dfrac{3}{4}\left( x+2 \right)=-1$ with 4. Then we separate the variables and the constants of the equation. 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. We solve the simplified form of the expression to find the value of the variable $x$.

Complete step by step answer:
The given equation $\dfrac{3}{4}\left( x+2 \right)=-1$ is an algebraic equation of $x$. we need to simplify the equation by solving the variables and the constants separately.
We first multiply both sides of the equation $\dfrac{3}{4}\left( x+2 \right)=-1$ with 4.
$\begin{align}
  & 4\times \dfrac{3}{4}\left( x+2 \right)=\left( -1 \right)\times 4 \\
 & \Rightarrow 3\left( x+2 \right)=-4 \\
\end{align}$
All the terms in the equation of \[3\left( x+2 \right)=-4\] are either variable of $x$ or a constant. We first separate the variables. We break the multiplication by multiplying 3 with $\left( x+2 \right)$.
$3\left( x+2 \right)=3x+6$. The expression change from \[3\left( x+2 \right)=-4\] to \[3x+6+4=0\]
There is only one variable which is $3x$.
Now we take the constants. There are two constants which are 6 and 4.
The addition gives $6+4=10$. The final solution becomes $3x+10=0$.
Now if we had to find the solution of the equation $3x+10=0$.
Now we take the variable on one side and the constants on the other side.
\[\begin{align}
  & 3x+10=0 \\
 & \Rightarrow 3x=-10 \\
 & \Rightarrow x=\dfrac{-10}{3} \\
\end{align}\]

Therefore, the solution of the equation $\dfrac{3}{4}\left( x+2 \right)=-1$ is \[x=\dfrac{-10}{3}\].

Note: We can verify the result of the equation $\dfrac{3}{4}\left( x+2 \right)=-1$ by taking the value of $x$ as \[x=\dfrac{-10}{3}\].
Therefore, the left-hand side of the equation becomes
$\dfrac{3}{4}\left( x+2 \right)=\dfrac{3}{4}\left( \dfrac{-10}{3}+2 \right)=\dfrac{3}{4}\times \dfrac{\left( -4 \right)}{3}=-1$
Thus, verified for the solution \[x=\dfrac{-10}{3}\] for the equation $\dfrac{3}{4}\left( x+2 \right)=-1$.