Question

Find the value of x from the following: $x - \dfrac{{20}}{{100}}x = 13500$

Answer 1

Hint: Find the least common denominator of all the fractions in the equation.
Multiply both sides of the equation by that LCD. This clears the fractions.
Isolate the variable terms on one side, and the constant terms on the other side.
Simplify both sides.
Use the multiplication or division property to make the coefficient on the variable equal to 1.

Complete step-by-step answer:
When we are solving equations, we must always remember that what's on the left side equals the right side. Therefore, any changes that we make to one side of the equation, we must make to the other side so that the equation stays equal and balanced. When solving single-variable equations, we try to isolate the variable on one side so that we can get a number which it's equal to on the other side. Therefore, everything we do to solve this equation must work towards getting just the variable on one side, and a number on the other side.
$x - \dfrac{{20}}{{100}}x = 13500$
Start by adding the terms with x together. Find the least common denominator (LCD) for the two fractions.
$ \Rightarrow \dfrac{{100x - 20x}}{{100}} = 13500$
$ \Rightarrow \dfrac{8}{{10}}x = 13500$
Multiply both sides of the equation by that LCD. This clears the fractions.
Now, multiply both sides by 10.
$ \Rightarrow 8x = 135000$
Isolate the variable terms on one side, and the constant terms on the other side.
Then divide both sides by 8.
$ \Rightarrow x = \dfrac{{135000}}{8} = 16875$

Therefore the value of x is 16875.

Note: One of the most common mistakes when you clear fractions is forgetting to multiply BOTH sides of the equation by the LCD. We can verify our answer by simply substituting the answer in the question. If the value satisfies the equation then the answer which we got is correct.