Question

Solve the following equation for x, $2.25x-125=3x+3.75$.

Answer 1

Hint: In order to solve this question, we will try to write the decimal digits into fractions, and then we will take the LCM to convert the fraction digits into whole numbers. After that, we will apply multiple arithmetic operations to get the value of x.

Complete step-by-step solution -
In this question, we have been asked to find the value of x for the given equation, $2.25x-125=3x+3.75$. To solve this equation, we will first convert all the decimal numbers, that are, 2.25 and 3.75 into fractions as $2.25=\dfrac{225}{100}$ and $3.75=\dfrac{375}{100}$. So, now we will get the equation as follows,
$\dfrac{225}{100}x-125=3x+\dfrac{375}{100}$
Now, we will take the LCM of both sides of the equation. So, we will get the equation as,
$\dfrac{225x-125\times 100}{100}=\dfrac{3\times 100x+375}{100}$
And we can further simplify and write as,
$\dfrac{225x-12500}{100}=\dfrac{300x+375}{100}$
We can see that here 100 is common in the denominator of both sides of the equation. So, we can cancel them out. Therefore, we get,
$225x-12500=300x+375$
Now, we will take all the variable terms on to the left-hand side and the constant terms to the right-hand side. So, we will get,
$225x-300x=12500+375$
Which can be further written as,
$-75x=12875$
Now, we will divide both sides of the equation by -75. So, we will get,
$\dfrac{-75x}{-75}=\dfrac{12875}{-75}$
And so, we get,
$x=\dfrac{-515}{3}$
Hence, we get the value of x for $2.25x-125=3x+3.75$ as $\dfrac{-515}{3}$.

Note: We can also solve this question without converting the decimals into fractions, but then the calculations with decimals will become tough and chances of errors will increase. So, it is preferable to convert the decimals into fractions and then whole numbers by taking the LCM.