Question

How do you solve \[5x + 3 = 23\]?

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).

Complete step-by-step solution:
Given, \[5x + 3 = 23\]
We have the unknown term in the left hand side of the equation, so we transpose the remaining terms to the right hand side of the equation. We transpose 3 to the right hand side of the equation by subtracting 3 on the right hand side of the equation.
\[ \Rightarrow 5x = 23 - 3\]
\[ \Rightarrow 5x = 20\]

Here 5 is multiplied to the variable (unknown value) ‘x’. We transpose 5 to the right hand side of the equation by dividing 5 on the right hand side of the equation.
\[ \Rightarrow x = \dfrac{{20}}{5}\]
\[ \Rightarrow x = 4\]

Note: We can check whether the obtained answer is correct or not. We substitute the obtained value in the given problem.
\[
  5(4) + 3 = 23 \\
  20 + 3 = 23 \\
   \Rightarrow 23 = 23 \\
\]
Hence the obtained answer is correct. If we want to transpose the addition number to any side of the equation we subtract it with the same number on both sides of the equation. Similarly if we want to transpose the negative number to any side of the equation we add with the same number on both sides of the equation. 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.