Question

Solve the equation: \[14y - 8 = 13\]

Answer 1

Hint: We will first consider the given equation and as we have to solve the equation for \[y\], we will add 8 on both sides of the equation and then simplify both left-hand and right-hand side of the equation. Next, we will divide both the sides of the equation by 14 which will give us the required answer.

Complete step-by-step answer:
We will first consider the given equation that is \[14y - 8 = 13\]
The objective is to solve the given equation for \[y\].
Now, to simplify the equation we will add 8 on both the sides of the equation that is the left-hand side and right-hand side of the equation.
Thus, we get,
\[ \Rightarrow 14y - 8 + 8 = 13 + 8\]
Now, we will further simplify the above equation to evaluate the value of \[y\].
\[ \Rightarrow 14y = 21\]
Next, we will divide the obtained equation by 14 to find the value of \[y\].
Thus, we get,
\[
   \Rightarrow \dfrac{{14y}}{{14}} = \dfrac{{21}}{{14}} \\
   \Rightarrow y = \dfrac{3}{2} \\
 \]
We can also verify the value of \[y\] by substituting the obtained value in the given expression,
Thus, we get,
\[
   \Rightarrow 14\left( {\dfrac{3}{2}} \right) - 8\mathop = \limits^? 13 \\
   \Rightarrow 21 - 8\mathop = \limits^? 13 \\
   \Rightarrow 13 = 13 \\
 \]
Thus, we can conclude that the value of \[y\] on solving the equation is \[\dfrac{3}{2}\].

Note: We can also take 8 from the left-hand side to the right-hand side of the equation and change the sign from negative to positive and add the numbers on the right-hand side of the equation and divide by 14 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 \[y\]. Do not make any calculation mistakes while simplifying the equation and substitute the value properly in the verification part.