Exercise 9.1
Question 1
(i)
$\begin{aligned} 2(3-2 x) &=13 \\ 6-4 x &=13 \\-4 x &=13-6 \\-4 x &=7 \\ x=-7 / 4 \end{aligned}$
ii) $\begin{aligned} \frac{3}{5} y-2=& 7 / 10 \\ \frac{3}{5} y &=7 / 10+2 \\ \frac{3}{5} y &=\frac{27}{10} \\ y &=\frac{27}{10} \times \frac{5}{3}=9 / 2 \end{aligned}$
= $9 / 2$
Question 2
i) $\frac{x}{2}=5+x / 3$
$\frac{x}{2}-\frac{x}{3}=5$
$\frac{3 x-2 x}{6}=5$
$x=5 \times 6$
$x=30$
ii) $2(x-3 / 2)=11$
$2 x-2\times 3 / 2=11$
$2 x-3=11$
$2 x=3+11$
$x=14 /2$
$x=7$
Question 3
i) $7(x-2)=2(2 x-4)$
$7 x-14=4 x-8$
$7 x-4 x=14-8$
$3 x=6$
$x= 6 / 2$
x = 2
ii)$21-3(x-7)=x+20$
$21-3 x+21=x+20$
$4 x=42-20$
$4 x=\frac{22}{11}$
x = 22\4
x = 11\2
Question 4
i) $3 x-\frac{1}{3}=2(x-1 / 2)+5$
$\frac{9 x-1}{3}=\frac{2(2 x-1)}{2}+5$
$\frac{9 x-1}{3}=2 x-1+5$
$\frac{9 x-1}{3}=2 x+4$
$9 x-1=6 x+12$
$9 x-6 x=12+1$
$3 x=13$
$x=13 / 3$
ii) $\frac{2 m}{3}-\frac{m}{5}=7$
$\frac{(2m) \times 5-3 m}{15}=7$
$\frac{10 m-3 m}{15}=7$
$\frac{7 m}{15}=7$
$m=7 \times \frac{15}{7}$
$m=15$
Question 5
i) $\frac{x+1}{5}-\frac{x-7}{2}=1$
$\frac{2(x+1)-5(x-7)}{10}=1$
$2 x+2-5 x+35=10$
$-3 x=10-35-2$
$-3 x=-27$
$x=\frac{-27}{-3}$
$x=9$
ii)
$\begin{aligned} \frac{3 p-2}{7}-\frac{p-2}{4}=2 & \\ \frac{4(3 p-2)-7(p-2)}{7 \times 4}=2 & \\ \frac{12 p-8-7 p+14}{28} &=2 \\ 5 p+6 &=56 \\ 5 p &=56-6 \\ 5 p &=50 \\ p &=50 / 5 \end{aligned}$
P = 10
Question 6
i) $\frac{1}{2}(x+5)-\frac{1}{3}(x-2)=4$
$\frac{3(x+5)-2(x-2)}{3 \times 2}=4$
$\frac{x+2 x+4=4 \times 6}{x+19}=24$
$x+19=24$
$x=24-19$
$x=5$
ii) $\frac{2 x-3}{1}-\frac{x-5}{2}=\frac{x}{6}$
$\frac{2(2 x-3)-6(x-5)}{6 \times 2}=\frac{x}{6}$
$4 x-6-6 x+30=$ $\frac{x}{6} \times {12}$
$-2 x+24 .=2 x$
$4 x=24$
$x=24 / 4$
x = 6
Question 7
i) $\frac{x-4}{7}-\frac{x+4}{5}=\frac{x+3}{7}$
$\frac{5(x-4)-7(x+4)}{7 \times 5}=\frac{x+3}{7}$
$5 x-20-7 x-28=\left(\frac{x+3}{7}\right) 35$
$\begin{aligned}-2 x-48 &=5 x+15 \\-48-15 &=5 x+2 x \\ 7 x &=-63 \\ x &=\frac{-63}{7} \\ x &=-9 \end{aligned}$
ii) $\frac{x-1}{5}+\frac{x-2}{2}=\frac{x}{3}+1$
$\frac{2(x-1)+5(x-2)}{5 \times 2}=\frac{x+3}{3}$
$\frac{2 x-2+5 x-10}{10}=\frac{x+3}{3}$
$\frac{7 x-12}{10}=\frac{x+3}{3}$
$3(7 x-12)=10(x+3)$
$21 x-36=10 x+30$
$11 x=66$
$x=\frac{66}{11}$
$x=6$
Question 8
i)
$\begin{aligned} y+1.2 y &=4.4 \\ 2.2 y &=4.4 \\ y &=\frac{4.4}{2.2} \\ y &=2 \end{aligned}$
ii) $15 \%$ of $x=21$
$\frac{15}{100} \times x=21$
$x=\frac{21 \times 100}{15}$
x = 140
Question 9
i) $2 p+20 \%$ of $(2 p-1)=7$
$2 p+\frac{20}{100}(2 p-1)=7$
$2 P+\frac{1}{5}(2 p-1)=7$
$5 \times 2 P+2 P-1=35$
$10 P+2 P=1+35$
$\begin{aligned} 12 p &=36 \\ p &=36 / 12 \\ p=3 \end{aligned}$
ii) $3(2 x-1)+25 \%$ of $x=97$
$3(2 x-1)+\frac{95}{100} \times x=97$
$6 x-3+\frac{1}{4} \times x=97$
$\frac{4(6 x-3)+x}{4}=97$
$24 x-12+x=97 \times 4$
$25 x=388+12$
$25 x=400$
$x=\frac{400}{25}$
x= 16
Question 10
$x^{4}-3 x^{3}-p x-5=2.3 .$
Given $x=-2$
$(-2)^{4}-3(-2)^{3}-p(-2)-5=23$
$16-3(-8)+2 p-5=23$
$16+24+2 p-5=23$
$2 P=23-35$
$2 p=-12$
p = -12\2
p = -6
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