Question

How do you solve \[5 - 2x = 3x - 7x + 25\] ?

Answer 1

Hint: In the given problem we need to solve this 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 one side and constants on the other side of the equation.

Complete step-by-step answer:
Given \[5 - 2x = 3x - 7x + 25\] .
We transpose \[ - 2x\] which is on the left side of the equation to the right hand side of the equation by adding \[2x\] to the right hand side of the equation.
 \[ \Rightarrow 5 = 3x - 7x + 25 + 2x\]
We transpose 25 which is on the right hand side of the equation to the left hand side of the equation by subtracting 25 to the left hand side of the equation.
 \[ \Rightarrow 5 - 25 = 3x - 7x + 2x\]
Rearranging the equation we have
 \[ \Rightarrow 3x - 7x + 2x = 5 - 25\]
Taking ‘x’ common we have
 \[ \Rightarrow x(3 - 7 + 2) = 5 - 25\]
 \[ \Rightarrow - 2x = - 20\]
Dividing by \[ - 2\] on both sides we have,
 \[ \Rightarrow x = \dfrac{{ - 20}}{{ - 2}}\]
 \[ \Rightarrow x = 10\] . This is the required answer.
So, the correct answer is “ x = 10”.

Note: We can check whether the given solution is correct or wrong. To check we need to substitute value of ‘x’ in the given problem we have
 \[5 - 2(10) = 3(10) - 7(10) + 25\]
 \[5 - 20 = 30 - 70 + 25\]
 \[ \Rightarrow - 15 = - 15\] .
Hence the given answer is correct.