Exercise 6A
Question 1
(a) 2x + 7 = 11
Sol :
2x=11-7
2x=4
$x=\frac{4}{2}=2$
∴x=2
(b) 8 + 5y = 23
Sol :
5y=23-8
5y=15
$y=\frac{15}{5}=3$
∴y=3
(c) 4x – 9 = 7
Sol :
4x=7+9
4x=16
$x=\frac{16}{4}=4$
∴x=4
(d) $\frac{y}{7}+1= 3$
Sol :
$\frac{y}{7}+1=3$
$\frac{y}{7}=3-1$
$\frac{y}{7}=2$
∴y=14
(e) $6 + \frac{t}{4} = 9$
Sol :
$6+\frac{t}{4}=9$
$\frac{t}{4}=9-6$
$\frac{t}{4}=3$
∴t=12
(f) $\frac{x}{3} + 9 = 1$
Sol :
$\frac{x}{3}+9=1$
$\frac{x}{3}=1-9$
$\frac{x}{3}=-8$
∴x=-24
Question 2
(a) 2x + 1 = x + 7
Sol :
2x-x=7-1
∴x=6
(b) 5x + 12 = 3x + 20
Sol :
5x-3x=20-12
2x=8
$x=\frac{8}{2}=4$
∴x=4
(c) 3y = 8y – 15
Sol :
3y-8y=-15
-5y=-15
$y=\frac{15}{5}=3$
∴y=3
(d) 6p – 18 = 5p – 7
Sol :
6p-18=5p-7
6p-5p=-7+18
∴p=11
(e) t + 10 = 20 – t
Sol :
t+t=20-10
2t=10
∴$t=\frac{10}{2}=5$
(f) 7z – 18 = 28 + 2z
Sol :
7z-2z=-28+18
5z=-10
$z=-\frac{10}{5}=-2$
Question 3
(a) 5x + 8 – 2x = 14
Sol :
5x-2x=14-8
3x=6
$x=\frac{6}{3}=2$
(b) 5(x – 7) = -10
Sol :
5x-35=-10
5x=-10+35
$x=\frac{25}{5}=5$
(c) -7x – 11 + 3x = 5
Sol :
-4x=5+11
-4x=16
$x=\frac{16}{-4}=-4$
(d) 6 = -2(7 – c)
Sol :
6=-14+2c
2c=6+14
2c=20
c=10
(e) 5(1 – 2w) + 8w = 15
Sol :
5-10w+8w=15
-2w=15-5
-2w=10
$-2w=\frac{10}{2}$
∴w=-5
(f) 17 = 3(p – 5) + 8
Sol :
17=39-15+8
3p=17+15-8
3p=24
$p=\frac{24}{3}=8$
Question 4
(a) 3x – 12 + 4x = 6x + 6
Sol :
3x+4x-6x=6+12
x=18
(b) 3(2x – 1) – 2x = -3
Sol :
6x-3-2x=-3
6x-2x=-3+3
4x=0
x=0
(c) 12 – 6x = 6(4 + 2x) + 6
Sol :
12-6x=24+12x+6
-6x-12x=24+6-12
-18x=18
x=-1
(d) 6 + 2(3x – 6) = 3(x + 2)
Sol :
6+6x-12=3x+6
6x-3x=6-6+12
3x=12
$x=\frac{12}{3}=4$
(e) 4(2x – 6) + 3 (x – 3) = 0
Sol :
8x-24+3x-9=0
8x+3x=24+9
11x=33
$x=\frac{33}{11}=3$
(f) 3(2y – 4) + 3y = 5(y – 4)
Sol :
6y-12+3y=5y-20
6y+3y-5y=-20+12
4y=-8
$y=\frac{-8}{4}=-2$
Question 5
8 + 2(5m – 8) + 3(m + 2) = 12 + 4(2m – 1)
Sol :8+10m-16+3m+6=12+8m-4
10m+3m-8m=12-4-8+16-6
5m=+10
$m=-\frac{10}{5}=2$
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