Question

Solve the equation: \[\dfrac{x}{3} + 1 = \dfrac{7}{{15}}\]

Answer 1

Hint: We will first consider the given equation and as we have to solve the equation for \[x\], we will subtract 1 on both sides of the equation and then simplify both left-hand and right-hand side of the equation. Next, we will multiply both the sides of the equation by 3 which will give us the required answer.

Complete step-by-step answer:
We will first consider the given equation that is \[\dfrac{x}{3} + 1 = \dfrac{7}{{15}}\]
The objective is to solve the given equation for \[x\].
Now, to simplify the equation we will subtract 1 on both the sides of the equation that is left-hand side and right-hand side of the equation.
Thus, we get,
\[ \Rightarrow \dfrac{x}{3} + 1 - 1 = \dfrac{7}{{15}} - 1\]
Now, we will further simplify the above equation by taking the L.C.M. on the right-hand side of the equation.
\[
   \Rightarrow \dfrac{x}{3} = \dfrac{{7 - 15}}{{15}} \\
   \Rightarrow \dfrac{x}{3} = \dfrac{{ - 8}}{{15}} \\
 \]
Next, we will multiply the obtained equation by 3 to find the value of \[x\].
Thus, we get,
\[
   \Rightarrow \dfrac{x}{3} \times 3 = \dfrac{{ - 8}}{{15}} \times 3 \\
   \Rightarrow x = \dfrac{{ - 8}}{5} \\
 \]
We can also verify the value of \[x\] by substituting the obtained value in the given expression,
Thus, we get,
\[
   \Rightarrow \dfrac{{\left( {\dfrac{{ - 8}}{5}} \right)}}{3} + 1\mathop = \limits^? \dfrac{7}{{15}} \\
   \Rightarrow \dfrac{{ - 8}}{{15}} + 1\mathop = \limits^? \dfrac{7}{{15}} \\
   \Rightarrow \dfrac{7}{{15}} = \dfrac{7}{{15}} \\
 \]
Thus, we can conclude that the value of \[x\] on solving the equation is \[\dfrac{{ - 8}}{5}\].

Note: We can also take 1 from the left-hand side to the right-hand side of the equation and change the sign from positive to negative and subtract the numbers on the right-hand side of the equation and multiply by 3 which will directly give us the result and work as an alternative method. As the given equation is a linear equation of first order, so we can directly solve it for the value of \[x\]. Do not make any calculation mistakes while simplifying the equation and substitute the value properly in the verification part.