Question

How do you solve \[\dfrac{x}{4} - 3 = 2\] ?

Answer 1

Hint: The given equation is the linear equation with one variable x that can be solve by add or subtract the necessary term from each side of the equation to isolate the term with the variable x, then multiply or divide each side of the equation by the appropriate value solve for the variable x while keeping the equation balanced then solve the resultant balance equation for the x value.

Complete step-by-step answer:
Consider given equation
 \[ \Rightarrow \,\,\,\dfrac{x}{4} - 3 = 2\]
Rearrange the equation by subtracting 2 from both sides of the equation, then
 \[ \Rightarrow \,\,\,\left( {\dfrac{x}{4} - 3} \right) - 2 = 0\]
Subtracting whole number from a fraction
Rewrite the whole number as a fraction using 1 as denominator, then
 \[ \Rightarrow \,\,\,\left( {\dfrac{x}{4} - \dfrac{3}{1}} \right) - 2 = 0\]
While subtracting two fractions the denominator should be the same or fractions should be a like fraction.
To subtract the fraction in above equation by taking 4 as LCM, then
  \[ \Rightarrow \,\,\,\left( {\dfrac{{x - 3\left( 4 \right)}}{4}} \right) - 2 = 0\]
 \[ \Rightarrow \,\,\,\left( {\dfrac{{x - 12}}{4}} \right) - 2 = 0\]
Again take 4 as LCM to subtract the RHS in above equation
 \[ \Rightarrow \,\,\,\dfrac{{x - 12 - 2\left( 4 \right)}}{4} = 0\]
 \[ \Rightarrow \,\,\,\dfrac{{x - 12 - 8}}{4} = 0\]
 \[ \Rightarrow \,\,\,\dfrac{{x - 12 - 8}}{4} = 0\]
 \[ \Rightarrow \,\,\,\dfrac{{x - 20}}{4} = 0\]
Multiply both side by 4, then
 \[ \Rightarrow \,\,\,x - 20 = 0\]
To solve the given equation for x by adding both side by 20, then
 \[ \Rightarrow \,\,\,x - 20 + 20 = 0 + 20\]
 \[\therefore \,\,\,x = 20\]
Hence, by solving the value of \[\dfrac{x}{4} - 3 = 2\] is 20
We can also verify the obtained answer is correct or not. By resubstituting the value of x which we has obtained in the given question we have
  \[\dfrac{x}{4} - 3 = 2\]
Here x=20, so we have
 \[ \Rightarrow \dfrac{{20}}{4} - 3 = 2\]
On dividing the number by 4 we get
 \[ \Rightarrow 5 - 3 = 2\]
On simplifying we get
 \[ \Rightarrow 2 = 2\]
LHS = RHS
Hence we have solved the equation and obtained the answer.
Therefore x=20.
So, the correct answer is “ x=20”.

Note: The given equation or expression is in the form of algebraic equation or expression, where it is a combination of variables and constants. Here the algebraic equation or expression contains the only one variable and that is x. so by using the simple arithmetic operations we can solve this kind of problem.