Question

Solve the following equation and verify the answer:
\[6x + 5 = 2x + 17\]

Answer 1

Hint: Here we have a linear equation with a variable ‘x’. Here we need to solve for ‘x’. 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 ‘x’ terms on one side and constants on the other side of the equation.

Complete step-by-step solution:
Given, \[6x + 5 = 2x + 17\].
We transpose \[5\] which is present in the left-hand side of the equation to the right-hand side of the equation by subtracting \[5\] on the right-hand side of the equation.
\[6x = 2x + 17 - 5\]
We transpose \[2x\] which is present in the right-hand side of the equation to the left-hand side of the equation by subtracting \[2x\] on the left-hand side of the equation.
\[6x - 2x = 17 - 5\]
We can see that the variable ‘x’ and the constants are separated, then
\[4x = 12\]
Divide the whole equation by 4
\[ \Rightarrow x = 3\]
This is the required answer.

Note: By simplifying we have obtained the answer for ‘x’. We can check whether the obtained value of ‘x’ is correct or not. To check we simply substitute the obtained value of ‘x’ in the given problem. If L.H.S is equal to R.H.S. then our answer is correct.
\[6x + 5 = 2x + 17\]
\[\Rightarrow 6\left( 3 \right) + 5 = 2\left( 3 \right) + 17\]
\[\Rightarrow 18 + 5 = 6 + 17\]
\[ \Rightarrow 23 = 23\]
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.