Question

How do you simplify \[\dfrac{x}{2} + 2 = 89\] ?

Answer 1

Hint: In the given problem we need to solve this for ‘x’. We take LCM on the left hand limit and we can solve this using the transposition method. The common transposition method is to do the same thing (mathematically) to both sides of the equation, with the aim of bringing like terms together and isolating the variable (or the unknown quantity). That is we group the ‘x’ terms one side and constants on the other side of the equation.

Complete step by step solution:
Given, \[\dfrac{x}{2} + 2 = 89\].
Now taking LCM and simplifying we have,
\[\dfrac{{x + 4}}{2} = 89\]
We transpose 2 to the right hand side of the equation by multiplying 2 on the right side of the equation,
\[x + 4 = 89 \times 2\]
Simplifying we have,
\[x + 4 = 178\]
We transpose 4 to the right hand side of the equation by subtracting 4 on the right hand side of the equation.
\[x = 178 - 4\]
Subtracting we have,
\[ \Rightarrow x = 174\]. This is the required answer.

Note: We can check whether the obtained answer is correct or not. We substitute the obtained answer in the problem.
Put \[x = 174\] in \[\dfrac{x}{2} + 2 = 89\].
\[\dfrac{{174}}{2} + 2 = 89\]
\[87 + 2 = 89\]
\[ \Rightarrow 89 = 89\]. Hence, the obtained answer is correct.
If we want to transpose the division number to the right side of the equation we multiply with the same number on the right side (vice versa). Similarly if we want to transpose an additional number to the right side of the equation we subtract it with the same number on the right side (vice versa). Follow the same procedure for these kinds of problems.