7.3.3 Buku Teks (Marilah Praktis) - Matematik Tingkatan 1, 2 dan 3

Soalan 10:
Selesaikan ketaksamaan linear serentak yang berikut.

\begin{array}{l} (a) 4 - 3 x \geq - 5 dan 3 x + 1 \geq - 11 \\ (b) \frac{3 x}{2} - 1 > 3 dan 3 - x \leq 7 \\ (c) \frac{2 x - 5}{3} \leq 3 dan \frac{5 - x}{2} \leq 1 \\ (d) \frac{x - 4}{3} \geq 2 - x dan \frac{3 x - 1}{4} < 2 \end{array}

Penyelesaian:
(a)

\begin{array}{l} 4 - 3 x \geq - 5 \\ - 3 x \geq - 5 - 4 \\ - 3 x \geq - 9 \\ 3 x \leq 9 \\ x \leq 3 \\ 3 x + 1 \geq - 11 \\ 3 x \geq - 11 - 1 \\ 3 x \geq - 12 \\ x \geq - 4 \end{array}

(b)

\begin{array}{l} \frac{3 x}{2} - 1 > 3 \\ 3 x - 2 > 6 \\ 3 x > 8 \\ x > \frac{8}{3} \\ 3 - x \leq 7 \\ - x \leq 4 \\ x \geq - 4 \end{array}

(c)

\begin{array}{l} \frac{2 x - 5}{3} \leq 3 \\ 2 x - 5 \leq 9 \\ 2 x \leq 14 \\ x \leq 7 \\ \frac{5 - x}{2} \leq 1 \\ 5 - x \leq 2 \\ - x \leq - 3 \\ x \geq 3 \end{array}

(d)

\begin{array}{l} \frac{x - 4}{3} \geq 2 - x \\ x - 4 \geq 6 - 3 x \\ x + 3 x \geq 6 + 4 \\ 4 x \geq 10 \\ x \geq \frac{10}{4} \\ x \geq \frac{5}{2} \\ \frac{3 x - 1}{4} < 2 \\ 3 x - 1 < 8 \\ 3 x < 9 \\ x < 3 \end{array}