Exercise 7A
Question 1
8x+14=5x+44
Sol :
⇒8x-5x=44-14
⇒3x=30
⇒x=10
Question 2
5m+7=10m–3
Sol :
⇒10m-5m=7+3
⇒5m=10
⇒m=2
Question 3
8y–14=6–2y
Sol :
⇒8y+2y=6+14
⇒10y=20
⇒y=2
Question 4
6p–21=p+4
Sol :
⇒6p-p=4+21
⇒5p=25
⇒p=5
Question 5
2(x–1)=12
Sol :
⇒2x-2=12
⇒2x=12+2
⇒x=7
Question 6
7+3(t+5)=31
Sol :
⇒7+3t+15=31
⇒3t=31-15-7
⇒3t=31-22=9
⇒t=3
Question 7
15+3(4x–30)=33
Sol :
⇒15+2x-90=33
⇒12x=33+90-15
⇒12x=90+18=108
⇒x=9
Question 8
5(x+2)–9(x–2)=0
Sol :
⇒5x+10-9x+18=0
⇒-4x=-(18+10)
⇒4x=28
⇒x=7
Question 9
3x+5=0.5x – 7
Sol :
⇒3x-0.5x=-7-5
⇒$\frac{25x}{10}=-12$
⇒$x=\frac{-12\times 10}{25}=\frac{-24}{5}$
⇒x=-4.8
Question 10
0.1(t–3)=0.15(t–4)
Sol :
⇒0.1t-0.3=0.15t-0.60
⇒+0.60-0.3=0.15t-0.1t
⇒0.30=0.05t
⇒t=6
Question 11
2(x – 2) + 5 = 4(x – 6) + 3
Sol :
⇒2x-4+5=4x-24+3
⇒-4+5+24-3=4x-2x
⇒-4-3+29=2x
⇒-7+29=2x
⇒22=2x
⇒x=11
Question 12
2m(m – 4) – 8 = m(2m – 12)
Sol :
⇒2m2-8m-8=2m2-12m
⇒12m-8m=8
⇒4m=8
⇒m=2
Question 13
3a + 2(a – 9) = 6 – (2a – 3)
Sol :
⇒3a+2a-18=6-2a+3
⇒5a+2a=18+9
⇒7a=27
⇒$a=\frac{27}{7}$
Question 14
8x – 2(2 + 3x) = 2(1 – 2x) – 3(x – 1)
Sol :⇒8a-4-6x=2-4x-3x+3
⇒2x+7x=5+4=9
⇒9x=9
⇒x=1
Question 15
$\frac{x}{2}+\frac{x}{3}+\frac{x}{6}=18$
Sol :
⇒$\frac{3x+2x+x}{6}=18$
⇒6x=18×6
⇒$x=\frac{18\times 6}{6}=18$
Question 16
$\frac{2x}{3}+\frac{x}{4}+\frac{x}{2}=34$
Sol :⇒$\frac{16x+6x+12x}{24}=34$
⇒x=24
Question 17
$\frac{p+1}{2}-\frac{2(p-1)}{3}=0$
Sol :
⇒$\frac{3(p+1)-4(p-1)}{6}=0$⇒-p+7=0
⇒p=7
Question 18
$6-\frac{3(n-7)}{4}=\frac{n}{2}$
Sol :
⇒$\frac{-3n}{4}+\frac{21}{4}=\frac{n}{2}-6$
⇒$\frac{3n}{4}+\frac{n}{2}=\frac{21}{4}+6$
⇒$\frac{3n+2n}{4}=\frac{21+24}{4}$
⇒5n=45
Question 19
$10-\frac{5(1+x)}{3}+\frac{3x+1}{5}=0$
Sol :
⇒$10-\frac{(5+5x)}{3}+\frac{3x+1}{5}=0$⇒$\frac{-5}{3}-\frac{5x}{3}+\frac{3x}{5}+\frac{1}{5}=-10$
⇒$\frac{-5x}{3}+\frac{3x}{5}=-10-\frac{1}{5}+\frac{5}{3}$
⇒$\frac{-25x+9x}{15}=\frac{-128}{15}$
⇒-16x=-128
⇒x=8
Question 20
$\frac{2b+1}{5}-\frac{b-1}{3}=1$
Sol :
⇒$\frac{6b+3-5b+5}{15}=1$⇒b+8=15
⇒b=15-8=7
Question 21
$\frac{5(1-z)}{3}-\frac{(3z-1)}{5}=\frac{1}{6}$
Sol :
⇒$\frac{5}{3}-\frac{5z}{3}-\frac{3z}{5}+\frac{1}{5}=\frac{1}{6}$
⇒$\frac{-25z-9z}{15}=\frac{1}{6}-\frac{5}{3}-\frac{1}{5}$
⇒$\frac{-34z}{15}=\frac{(1\times 5)-(5\times 10)-1\times 6}{30}$
⇒$\frac{-34z}{15}=\frac{5-50-6}{30}$
⇒$\frac{-34z}{15}=\frac{5-56}{30}$
⇒$-34z=\frac{-51}{30}\times 15$
⇒$z=\frac{-51}{2 \times -34}$
⇒$z=\frac{51}{68}=\frac{3}{4}$
Question 22
$\frac{x+5}{15}-\frac{x-5}{10}=1+\frac{2x}{15}$
Sol :
⇒$\frac{x}{15}+\frac{5}{15}-\frac{x}{10}+\frac{5}{10}=1+\frac{2x}{15}$⇒$\frac{x}{15}-\frac{x}{10}-\frac{2x}{15}=-\frac{1}{3}-\frac{1}{2}+\frac{1}{1}$
Question 23
$\frac{3x-4}{6}-\frac{2x+3}{8}=\frac{2x-7}{24}$
Sol :
⇒$\frac{12x-16-6x-9}{24}=\frac{2x-7}{24}$
⇒12x-16-6x-9=2x-7
⇒12x-6x-2x=-7+25
⇒12x-8x=+18
⇒4x=18
⇒$x=\frac{18}{4}=\frac{9}{2}$
Question 24
$(x+0.5) +\frac{1}{2}\left(3x – \frac{1}{3}\right) = \frac{1}{3}(x+1)$
Sol :
⇒$x+0.5+\frac{3x}{2}-\frac{1}{6}=\frac{x}{3}+\frac{1}{3}$
⇒$x+\frac{3x}{2}-\frac{x}{2}=\frac{1}{3}+\frac{1}{6}-0.5$
⇒$\frac{2x+3x-x}{2}=\frac{1}{3}+\frac{1}{6}-\frac{1}{2}$
⇒$\frac{4x}{2}=\frac{3-3}{6}$
⇒$\frac{4x}{2}=0$
⇒x=0
Question 25
$\frac{9x-5}{7}=\frac{6x+2}{5}$
Sol :
⇒45x-25=42x+14⇒45x-42x=14+25
⇒3x=39
⇒x=13
Question 26
$\frac{7x-10}{5}=\frac{8x-5}{7}$
Sol :
⇒49x-70=40x-25⇒49x-40x=70-25=45
⇒9x=45
⇒x=5
Question 27
$\frac{2x-7}{x+4}=\frac{3}{4}$
Sol :
⇒4(2x-7)=3(x+4)⇒8x-28=3x+12
⇒8x-3x=28+12
⇒5x=40
⇒$x=\frac{40}{5}=8$
Question 28
$\frac{3m+4}{2-6m}=\frac{-2}{5}$
Sol :
⇒15m-12m=-4-20
⇒3m=-24
⇒m=-8
Question 29
$\frac{2n-3}{2n-1}=\frac{3n-1}{3n+1}$
Sol :
⇒(2n-3)(3n+1)=(2n-1)(3n-1)
⇒6x2+2n-9n-3=6x2-2n-3n+1
⇒-7n+5n=1+3
⇒-2n=4⇒n=-2
No comments:
Post a Comment