Question

How do you solve $-5=\dfrac{3}{4}x-2$?

Answer 1

Hint: We multiply the equation on both sides with 4. The we separate the variables and the constants of the equation $3x-8=-20$. 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 multiply the given equation $-5=\dfrac{3}{4}x-2$ with 4 and get
$\begin{align}
  & \left( -5 \right)\times 4=4\left( \dfrac{3}{4}x-2 \right) \\
 & \Rightarrow 3x-8=-20 \\
\end{align}$
The given equation $3x-8=20$ 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 $3x-8=-20$ are either variable of $x$ or a constant. We first separate the variables.
We take the constants all together to solve it.
$\begin{align}
  & 3x-8=-20 \\
 & \Rightarrow 3x=-20+8 \\
\end{align}$
There is two such constants which are $-20$ and 8.
Now we apply the binary operation of addition to get
$\Rightarrow 3x=-20+8=-12$
The binary operation between them is addition which gives us $3x=-12$.
Now we divide both sies of the equation with 3 to get
\[\begin{align}
  & 3x=-12 \\
 & \Rightarrow \dfrac{3x}{3}=\dfrac{-12}{3} \\
 & \Rightarrow x=-4 \\
\end{align}\]
We can also solve the equation directly.
$\begin{align}
  & -5=\dfrac{3}{4}x-2 \\
 & \Rightarrow \dfrac{3x}{4}=-5+2 \\
\end{align}$
We take the constants fractions together.
$\Rightarrow \dfrac{3x}{4}=-5+2=-3$
Now cross-multiplying we get
$\begin{align}
  & \Rightarrow \dfrac{3x}{4}=-3 \\
 & \Rightarrow x=\dfrac{\left( -3 \right)\times 4}{3}=-4 \\
\end{align}$
The solution is \[x=-4\].

Note: We can verify the result of the equation $-5=\dfrac{3}{4}x-2$ by taking the value of as \[x=-4\].
Therefore, the right-hand side of the equation $-5=\dfrac{3}{4}x-2$ becomes
$\dfrac{3}{4}x-2=\dfrac{3}{4}\times \left( -4 \right)-2=-3-2=-5$
Thus, verified for the equation $-5=\dfrac{3}{4}x-2$ the solution is \[x=-4\].