Question

How do you solve \[\dfrac{{x + 5}}{7} = \dfrac{5}{3}\]?

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 solution:
Given, \[\dfrac{{x + 5}}{7} = \dfrac{5}{3}\].
We transpose ‘7’ which is present in the left hand side of the equation to the right hand side of the equation by multiplying ‘7’ on the right hand side of the equation.
\[x + 5 = \dfrac{5}{3} \times 7\]
We transpose 5 to the right hand side of the equation by subtracting 5 on the right hand side of the equation.
\[x = \left( {\dfrac{5}{3} \times 7} \right) - 5\]
We can see that the variable is on the left hand side and the remaining constant is on the right hand side of the equation. We simplify the terms in the right hand side of the equation.
\[x = \dfrac{{35}}{3} - 5\].
Taking LCM and simplifying we have,
\[
x = \dfrac{{35 - (3 \times 5)}}{3} \\
x = \dfrac{{35 - 15}}{3} \\
\]
\[ \Rightarrow x = \dfrac{{20}}{3}\]. This is the exact form.
In decimal form,
\[ \Rightarrow x = 6.667\]. This is the required answer.

Note: We can check whether the obtained solution is correct or wrong. All we need to do is substituting the value of ‘x’ in the given problem.
\[\dfrac{{\left( {\dfrac{{20}}{3}} \right) + 5}}{7} = \dfrac{5}{3}\]
Simplifying the numerator of the left hand side of the equation,
\[
\dfrac{{\left( {\dfrac{{20 + 15}}{3}} \right)}}{7} = \dfrac{5}{3} \\
\dfrac{{\left( {\dfrac{{35}}{3}} \right)}}{7} = \dfrac{5}{3} \\
\]
Rearranging we have,
\[\dfrac{{35}}{{3 \times 7}} = \dfrac{5}{3}\]
Cancelling the terms we have
\[ \Rightarrow \dfrac{5}{3} = \dfrac{5}{3}\].
Hence the obtained answer is correct.
If we want to transpose a positive number to the other side of the equation we subtract the same number on that side (vice versa). 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.