(a)

\begin{align} 4x & < 2x + 3 \\ 4x - 2x & < 3 \\ 2x & < 3 \\ x & < {3 \over 2} \end{align}

(b)

\begin{align} 3x & > 7x + 10 \\ 3x - 7x & > 10 \\ -4x & > 10 \\ x & < {10 \over -4} \\ x & < -2.5 \end{align}

(c)

\begin{align} 5x & \ge 2(2x + 3) \\ 5x & \ge 4x + 6 \\ 5x - 4x & \ge 6 \\ x & \ge 6 \end{align}

(d)

\begin{align} 2x + 5 & \le 6x - 13 \\ 2x - 6x & \le -13 - 5 \\ - 4x & \le -18 \\ x & \ge {-18 \over -4} \\ x & \ge 4.5 \end{align}

\begin{align} 2x - 3 & \le 7 &&& 2x + 1 & \ge - 3x - 4 \\ 2x & \le 7 + 3 &&& 2x + 3x & \ge - 4 - 1 \\ 2x & \le 10 &&& 5x & \ge - 5 \\ x & \le {10 \over 2} &&& x & \ge {-5 \over 5} \\ x & \le 5 &&& x & \ge -1 \end{align}
$$ -1 \le x \le 5 $$

\begin{align} {y - 2 \over 3} & < {2y + 1 \over 5} &&& {2y + 1 \over 5} & \le 3 \\ {5(y - 2) \over 15} & < {3(2y + 1) \over 15} &&& {2y + 1 \over 5} & \le {15 \over 5} \\ 5(y - 2) & < 3(2y + 1) &&& 2y + 1 & \le 15 \\ 5y - 10 & < 6y + 3 &&& 2y & \le 15 - 1 \\ 5y - 6y & < 3 + 10 &&& 2y & \le 14 \\ -y & < 13 &&& y & \le {14 \over 2} \\ y & > -13 &&& y & \le 7 \end{align}
$$ -13 < y \le 7 $$

\begin{align} 20 \text{ cents} & = \$ 0.20 \\ \\ 50 \text{ cents} & = \$ 0.50 \\ \\ \text{Let } x \text{ represent } & \text{the number of 50-cent coins} \\ \\ \text{No. of 20-cent coins} & = 48 - x \end{align}
\begin{align} \text{No. of 20 cent coins} & \ge 2 \times \text{No. of 50 cent coins} &&& \text{Total value of coints} & \ge \$12 \\ 48 - x & \ge 2 \times x &&& 0.20(48 - x) + 0.50(x) & \ge 12 \\ 48 - x & \ge 2x &&& 9.6 - 0.2x + 0.5x & \ge 12 \\ - x - 2x & \ge -48 &&& -0.2x + 0.5x & \ge 12 - 9.6 \\ -3x & \ge - 48 &&& 0.3x & \ge 2.4 \\ x & \le {-48 \over -3} &&& x & \ge {2.4 \over 0.3} \\ x & \le 16 &&& x & \ge 8 \end{align}
\begin{align} 8 \le x \le 16 & \\ \\ \text{If } x = 10, & \\ \text{No. of 50 cent coins} & = 10 \\ \text{No. of 20 cent coins} & = 48 - 10 = 38 \end{align}