Equations Reducible to the Linear Form

Sometimes there are some equations which are not linear equations but can be reduced to the linear form and then can be solved by the above methods.

Example

Solve \mathrm{\dfrac{x+1}{2x+3}=\dfrac{3}{8}}

Solution

This is not a linear equation but can be reduced to linear form

Step 1: Multiply both the sides by Solve \mathrm{(2x + 3)}.

\mathrm{\dfrac{x+1}{2x+3}\times(2x+3)=\dfrac{3}{8}\times(2x+3)}

\mathrm{x+1=\dfrac{3(2x+3)}{8}}

Now, this is a linear equation.

Step 2: Multiply both the sides by 8.

\mathrm{8(x + 1) = 3(2x + 3)}\\ \\ \mathrm{8x + 8 = 6x + 9}\\ \\ \mathrm{8x - 6x = 9 - 8}\\ \\ \mathrm{2x = 1}\\ \\ \mathrm{x = \dfrac{1}{2}}

So the solution for the equation is \mathrm{x = \dfrac{1}{2}}.

Example

Sum of two numbers is 74. One of the numbers is 10 more than the other. What are the numbers?

Solution


Let one of the numbers be x.
Then the other number is x + 10.

Given that the sum of the two numbers is 74.
So, \mathrm{x+(x+10) =74}


\mathrm{\Rightarrow 2x+10=74 }\\ \\ \mathrm{\Rightarrow 2x=74-10=64}\\ \\ \mathrm{\Rightarrow x=\dfrac{64}{2}}\\ \\ =32


One of the number is 32 and the other number is 42.

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