Question

Each Equation is followed by the values of the variable. Decide whether these values are the solutions of that equation.
(1) x − 4 = 3, x =−1, 7,−7
(2) 9m = 81, m = 3, 9, −3
(3) 2a + 4 = 0, a = 2, −2, 1
(4) 3 − y = 4, y = −1, 1, 2

Answer 1

(1) x − 4 = 3, x =−1, 7,−7

$$\begin{gathered} x-4=3 \\ \Rightarrow x-4+4=3+4 \\ \Rightarrow x=7 \end{gathered}$$

Hence, x = 7 is the solution of the equation.

(2) 9m = 81, m = 3, 9, −3

$$\begin{gathered} 9m=81 \\ \mathrm{Dividing}\mathrm{both}\mathrm{sides}\mathrm{by}9 \\ \Rightarrow \frac{9m}{9}=\frac{81}{9} \\ \Rightarrow m=9 \end{gathered}$$

Hence, m = 9 is the solution of the equation.

(3) 2a + 4 = 0, a = 2, −2, 1

$$\begin{gathered} 2a+4=0 \\ \Rightarrow 2a+4-4=-4 \\ \Rightarrow 2a=-4 \\ \mathrm{Dividing}\mathrm{both}\mathrm{sides}\mathrm{by}2 \\ \Rightarrow \frac{2a}{2}=\frac{-4}{2} \\ \Rightarrow a=-2 \end{gathered}$$

Hence, a = −2 is the solution of the equation.

(4) 3 − y = 4, y = −1, 1, 2

$$\begin{gathered} 3-y=4 \\ \Rightarrow 3-y+y=4+y \\ \Rightarrow 3=4+y \\ \Rightarrow 3-4=4+y-4 \\ \Rightarrow -1=y \end{gathered}$$

Hence, y = −1 is the solution of the equation.