Soalan 3(a):
Selesaikan yang berikut.
(a) Diberi c = 4d + 8, hitung
(i) nilai c apabila d = 2
(ii) nilai d apabila c = 10
Penyelesaian:
(a)(i)
$$ \begin{aligned} &\text { nilai } c \text { apabila } d=2\\ &\begin{aligned} c & =4 d+8 \\ c & =4(2)+8 \\ & =16 \end{aligned} \end{aligned} $$
(a)(ii)
$$ \begin{aligned} & \text { nilai } d \text { apabila } c=10 \\ & c=4 d+8 \\ & 10=4 d+8 \\ &-4 d=8-10 \\ &-4 d=-2 \\ & d=\frac{-2}{-4} \\ &=\frac{1}{2} \end{aligned} $$
Selesaikan yang berikut.
(a) Diberi c = 4d + 8, hitung
(i) nilai c apabila d = 2
(ii) nilai d apabila c = 10
Penyelesaian:
(a)(i)
$$ \begin{aligned} &\text { nilai } c \text { apabila } d=2\\ &\begin{aligned} c & =4 d+8 \\ c & =4(2)+8 \\ & =16 \end{aligned} \end{aligned} $$
(a)(ii)
$$ \begin{aligned} & \text { nilai } d \text { apabila } c=10 \\ & c=4 d+8 \\ & 10=4 d+8 \\ &-4 d=8-10 \\ &-4 d=-2 \\ & d=\frac{-2}{-4} \\ &=\frac{1}{2} \end{aligned} $$
Soalan 3(b):
Selesaikan yang berikut.
(b) Diberi 4p = 18 − 5q, hitung
(i) nilai p apabila q = 2
(ii) nilai q apabila p = 2
Penyelesaian:
(b)(i)
$$ \begin{aligned} & \text { nilai } p \text { apabila } q=2 \\ & 4 p=18-5 q \\ & 4 p=18-5(2) \\ & 4 p=18-10 \\ & 4 p=8 \\ & p=\frac{8}{4} \\ & p=2 \end{aligned} $$
(b)(ii)
$$ \begin{aligned} & \text { nilai } q \text { apabila } p=2 \\ & 4 p=18-5 q \\ & 4(2)=18-5 q \\ & 8=18-5 q \\ & 5 q=18-8 \\ & 5 q=10 \\ & q=\frac{10}{5} \\ & q=2 \end{aligned} $$
Selesaikan yang berikut.
(b) Diberi 4p = 18 − 5q, hitung
(i) nilai p apabila q = 2
(ii) nilai q apabila p = 2
Penyelesaian:
(b)(i)
$$ \begin{aligned} & \text { nilai } p \text { apabila } q=2 \\ & 4 p=18-5 q \\ & 4 p=18-5(2) \\ & 4 p=18-10 \\ & 4 p=8 \\ & p=\frac{8}{4} \\ & p=2 \end{aligned} $$
(b)(ii)
$$ \begin{aligned} & \text { nilai } q \text { apabila } p=2 \\ & 4 p=18-5 q \\ & 4(2)=18-5 q \\ & 8=18-5 q \\ & 5 q=18-8 \\ & 5 q=10 \\ & q=\frac{10}{5} \\ & q=2 \end{aligned} $$
Soalan 3(c):
Selesaikan yang berikut.
$$ \text { Diberi } \frac{1}{3} m=\frac{2}{3} n+8 \text {, hitung } $$
(i) nilai m apabila n = −15
(ii) nilai n apabila m = 30
Penyelesaian:
(c)(i)
$$ \begin{aligned} & \text { nilai } m \text { apabila } n=-15 \\ & \frac{1}{3} m=\frac{2}{3} n+8 \\ & \frac{1}{3} m=\frac{2}{3}(-15)+8 \\ & \frac{1}{3} m=-10+8 \\ & \frac{1}{3} m=-2 \\ & m=(-2)(3) \\ & m=-6 \end{aligned} $$
(c)(ii)
$$ \begin{aligned} & \text { nilai } n \text { apabila } m=30 \\ & \frac{1}{3} m=\frac{2}{3} n+8 \\ & \begin{aligned} \frac{1}{3}(30) & =\frac{2}{3} n+8 \\ 10 & =\frac{2}{3} n+8 \\ 10-8 & =\frac{2}{3} n \\ 2 & =\frac{2}{3} n \\ 2 \times \frac{3}{2} & =n \\ 3 & =n \\ n & =3 \end{aligned} \end{aligned} $$
Selesaikan yang berikut.
$$ \text { Diberi } \frac{1}{3} m=\frac{2}{3} n+8 \text {, hitung } $$
(i) nilai m apabila n = −15
(ii) nilai n apabila m = 30
Penyelesaian:
(c)(i)
$$ \begin{aligned} & \text { nilai } m \text { apabila } n=-15 \\ & \frac{1}{3} m=\frac{2}{3} n+8 \\ & \frac{1}{3} m=\frac{2}{3}(-15)+8 \\ & \frac{1}{3} m=-10+8 \\ & \frac{1}{3} m=-2 \\ & m=(-2)(3) \\ & m=-6 \end{aligned} $$
(c)(ii)
$$ \begin{aligned} & \text { nilai } n \text { apabila } m=30 \\ & \frac{1}{3} m=\frac{2}{3} n+8 \\ & \begin{aligned} \frac{1}{3}(30) & =\frac{2}{3} n+8 \\ 10 & =\frac{2}{3} n+8 \\ 10-8 & =\frac{2}{3} n \\ 2 & =\frac{2}{3} n \\ 2 \times \frac{3}{2} & =n \\ 3 & =n \\ n & =3 \end{aligned} \end{aligned} $$
Soalan 3(d):
Selesaikan yang berikut.
$$ \text { Diberi } \sqrt{4 m}=\frac{n^2-5}{2} \text {, hitung } $$
(i) nilai n apabila m = 4
(ii) nilai m apabila n = 2
Penyelesaian:
(d)(i)
$$ \begin{aligned} &\text { nilai } n \text { apabila } m=4\\ &\begin{aligned} \sqrt{4 m} & =\frac{n^2-5}{2} \\ \sqrt{4(4)} & =\frac{n^2-5}{2} \\ 4 & =\frac{n^2-5}{2} \\ 8 & =n^2-5 \\ 8+5 & =n^2 \\ 13 & =n^2 \\ \sqrt{13} & =n \\ n & =\sqrt{13} \end{aligned} \end{aligned} $$
(d)(ii)
$$ \begin{aligned} &\text { nilai } m \text { apabila } n=2\\ &\begin{aligned} \sqrt{4 m} & =\frac{n^2-5}{2} \\ \sqrt{4 m} & =\frac{(2)^2-5}{2} \\ \sqrt{4 m} & =\frac{4-5}{2} \\ \sqrt{4 m} & =-\frac{1}{2} \\ 4 m & =\left(-\frac{1}{2}\right)^2 \\ 4 m & =\frac{1}{4} \\ m & =\frac{1}{4 \times 4} \\ m & =\frac{1}{16} \end{aligned} \end{aligned} $$
Selesaikan yang berikut.
$$ \text { Diberi } \sqrt{4 m}=\frac{n^2-5}{2} \text {, hitung } $$
(i) nilai n apabila m = 4
(ii) nilai m apabila n = 2
Penyelesaian:
(d)(i)
$$ \begin{aligned} &\text { nilai } n \text { apabila } m=4\\ &\begin{aligned} \sqrt{4 m} & =\frac{n^2-5}{2} \\ \sqrt{4(4)} & =\frac{n^2-5}{2} \\ 4 & =\frac{n^2-5}{2} \\ 8 & =n^2-5 \\ 8+5 & =n^2 \\ 13 & =n^2 \\ \sqrt{13} & =n \\ n & =\sqrt{13} \end{aligned} \end{aligned} $$
(d)(ii)
$$ \begin{aligned} &\text { nilai } m \text { apabila } n=2\\ &\begin{aligned} \sqrt{4 m} & =\frac{n^2-5}{2} \\ \sqrt{4 m} & =\frac{(2)^2-5}{2} \\ \sqrt{4 m} & =\frac{4-5}{2} \\ \sqrt{4 m} & =-\frac{1}{2} \\ 4 m & =\left(-\frac{1}{2}\right)^2 \\ 4 m & =\frac{1}{4} \\ m & =\frac{1}{4 \times 4} \\ m & =\frac{1}{16} \end{aligned} \end{aligned} $$