Question

Solve \[3y + 5 = 44\]

Answer 1

Hint: We look at the equation and choose the variable whose value we need to find. Shift the required values to the opposite side and cancel the required terms and calculate the value of the variable.

Complete step-by-step solution:
We are given the equation\[3y + 5 = 44\]...............… (1)
Since this equation consists of only one variable i.e. ‘y’ along with other constant values on both sides of the equation, we have to find the value of ‘y’. The equation (1) is a linear equation in one variable where the variable is ‘y’ and by shifting terms and applying arithmetic operations like addition, subtraction, multiplication and division we can calculate the value of the variable.
Shift all constant values in equation (1) to one side of the equation
\[ \Rightarrow 3y = 44 - 5\]
Calculate the difference of numbers in right hand side of the equation
\[ \Rightarrow 3y = 39\]
Divide both sides of the equation by 3
\[ \Rightarrow \dfrac{{3y}}{3} = \dfrac{{39}}{3}\]
Since we can write\[39 = 3 \times 13\], substitute the value of numerator in right hand side of the equation as\[39 = 3 \times 13\]
\[ \Rightarrow \dfrac{{3y}}{3} = \dfrac{{3 \times 13}}{3}\]
Cancel same factors from numerator and denominator on both sides of the equation
\[ \Rightarrow y = 13\]

\[\therefore \]The value of y is 13

Note: Students are likely to make mistakes while shifting the values from one side of the equation to another side of the equation as they forget to change the sign of the value shifted. Keep in mind we always change the sign of the value from positive to negative and vice versa when shifting values from one side of the equation to another side of the equation. Also students should factorize the numerator in terms of the denominator if possible so it is easier to cancel out the factors between the numerator and denominator.