Question

Find the value of x
\[0.25 + \dfrac{{1.95}}{x} = 0.9\]

Answer 1

Hint: Linear equations are the equation whose variables have the highest exponential power as one, also known as the first-degree equation. A linear equation can have more than one variable. As we can see in the question, the variable x is in the denominator, bring the variable to the numerator by using cross multiplication where, cross multiplication is referred to as the method of multiplying the denominator of one side to the numerator of the other side and the numerator of one side to the denominator of the other side.

Complete step by step answer:
Write the given equation into a linear equation form keeping the variable in the LHS. Hence we can write:
\[
  \dfrac{{1.95}}{x} = 0.9 - 0.25 \\
  \dfrac{{1.95}}{x} = 0.65 \\
 \]
Now, cross multiply the variable \[x\]in the denominator with the numerator to the other side of the equation, we get:
\[1.95 = 0.65x\]
Now, bring the variable to the LHS:
\[0.65x = 1.95\]
Hence, the value of variable x can be calculated as:
\[
  x = \dfrac{{1.95}}{{0.65}} \\
   = 3 \\
 \]
Hence, the value of $x$ satisfying the equation \[0.25 + \dfrac{{1.95}}{x} = 0.9\] is 3.
Additional Information: A linear equation can be written in the form of \[{a_1}{x_1} + {a_2}{x_2} + ......... + {a_n}{x_n} + b = 0\]where the variable of the equation is \[{x_1},{x_2}..............{x_n}\] and \[{a_1},{a_2}..............{a_n}\] being their coefficients, whereas b is constant in the equation. In the linear equations, always try to keep all variables on one side, preferably on LHS, as it is convenient to find the value of variables.

Note: To find the value of a variable in an equation, always try to keep that variable in the Left-Hand Side of an equation. Cross multiplying can also be referred to as the method of removing the fractional terms in an equation by multiplying each term present in the denominator by each term present in the numerator.