Question

How do you solve \[17p - 2 = 49\]?

Answer 1

Hint: Here we have a linear equation with a variable ‘p’. Here we need to solve for ‘p’. We can solve this using the transposition method. The common transposition method is to do the same thing (mathematically) to both sides of the equation, with the aim of bringing like terms together and isolating the variable (or the unknown quantity). That is we group the ‘p’ terms on one side and constants on the other side of the equation.

Complete step-by-step solution:
Complete step by step solution:
Given, \[17p - 2 = 49\].
We transpose \[ - 2\] which is present in the left-hand side of the equation to the right-hand side of the equation by adding \[2\]on the right-hand side of the equation.
\[17p = 49 + 2\]
\[\Rightarrow 17p = 51\]
We can see that the variable ‘p’ and the constants are separated, then
We transpose 17 to the right-hand side of the equation by dividing 17 on the right-hand side,
\[p = \dfrac{{51}}{{17}}\]
\[ \Rightarrow p = 3\]

Note: By simplifying we have obtained the answer for ‘p’. We can check whether the obtained value of ‘p’ is correct or not. To check we simply substitute the obtained value of ‘p’ in the given problem. If L.H.S is equal to R.H.S. then our answer is correct.
\[17p - 2 = 49\]
\[17(3) - 2 = 49\]7
\[51 - 2 = 49\]
\[ \Rightarrow 49 = 49\]
Hence the obtained answer is correct.
In the above, we did the transpose of addition and subtraction. Similarly, if we have multiplication, we use division to transpose. If we have division, we use multiplication to transpose. Follow the same procedure for these kinds of problems.