\begin{tabular}{c}\hline SOLVING EQUATIONS \\ \hline \( \begin{array}{c}\text { Simplify Each Side } \\ \text { by combining like terms }\end{array} \) \\ \hline \( \begin{array}{c}\text { Move Variables } \\ \text { to one side }\end{array} \) \\ \hline Solve \\ \hline Using inverse operations \\ \hline\end{tabular}

Describe the steps involved in finding the inverse of a function algebraically.

\( ( a + b ) ( a - b ) = a ^ { r } - b ^ { r } \)

ection-A consists of 20 questions of 1 mark each. The equation which has no real roots is \( \begin{array}{llll}\text { (a) } 3 x^{2}=8 x-2 & \text { (b) } x^{2}-11 x=16 & \text { (c) } 7 x^{2}-1=-8 x & \text { (d) } 2 x^{2}+5 x+6=0\end{array} \)

The ring \( \mathbb{Z} \) has no nontrivial idempotent elements, whereas \( \mathbb{Z} \times \mathbb{Z} \) has the idernpotent elements \( (1,0) \) and \( (0,1) \).

(a) \( \frac{2 x-3}{4}=5 \)