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Solve for \[x\]: \[\dfrac{{x - 3}}{5} - 2 = - 1\]

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Last updated date: 13th Jul 2024
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Answer
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Hint: Here we are asked to solve the given equation to find the value of \[x\]. Any simple equation can be solved by using the transposition method. In this method, we will try to keep the unknown variable on one side of the equation and transfer the other terms to the other side. Then by calculating that side we will get the value of the unknown variable.

Complete step by step answer:
It is given that \[\dfrac{{x - 3}}{5} - 2 = - 1\] we aim to solve this equation to find the value of \[x\].
We know that a simple equation can be solved by three methods one of the most efficient methods is the transposition method. In this method, the unknown variable will be kept alone on one side of the equation and the other terms will be transferred to the other side. Then by evaluating the other side we will get the value of the unknown variable.
Let us consider the given equation \[\dfrac{{x - 3}}{5} - 2 = - 1\], here we first transfer the term \[ - 2\] to the other side.
\[\dfrac{{x - 3}}{5} - 2 = - 1 \Rightarrow \dfrac{{x - 3}}{5} = 2 - 1\]
On simplifying the above equation, we get
\[ \Rightarrow \dfrac{{x - 3}}{5} = 1\]
Now from the above equation let us transfer the term \[5\] at the denominator of the fraction part to the other side.
\[ \Rightarrow x - 3 = 1 \times 5\]
Now let us simplify it.
\[ \Rightarrow x - 3 = 5\]
At last, let us transfer the term \[ - 3\] to the other side.
\[x = 5 + 3\]
On simplifying the above, we get
\[x = 8\]
Thus, we have got the value of the unknown variable \[x\] as \[8\].

Note:
Any simple equation can be solved by using three main methods: the trial-and-error method, the systematic method, and the transposition method. Here we have used the transposition method to solve this problem because it is more time-efficient than the other two methods.