Question

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Answer 1

a)
3(x-2) - (1 - x) = 13
3x - 6 - 1 + x = 13
4x - 7 = 13
4x = 13 +7
4x = 20
x = 20/4
x = 5

b)
6 (4 - t) - 55 = - 5(2t + 3)
24 - 6t - 55 = - 10t - 15
10t - 6t = - 15 + 55 - 24
4t = 40 - 24
4t = 16
t = 16/4
t = 4 

c)
5 - 4(x - 1) = 4x - 3(4x - 1) - 4
5 - 4x + 4 = 4x - 12x + 3 - 4
- 4x + 9 = - 8x - 1
- 4x + 8x = - 1 - 9
4x = -10
x = -10/4
x = - 5/2

d)
y - [y - (2 - y) - 1] = - (1 - y)
y - [y - 2 + y - 1] = - 1 + y
y - [2y - 3] = - 1 + y
y - 2y + 3 = - 1 + y
y - 2y - y = - 1 - 3
-2y = - 4
2y = 4
y = 4/2
y = 2

e)
5[2(t + 4) - t] = 2 (3t + 19)
5[2t + 8 - t] = 6t + 38
5[t + 8] = 6t + 38
5t + 40 = 6t + 38
40 - 38 = 6t - 5t
2 = t
t = 2

f)
4 (2y - 1) = 3 (5y - 2) - 5
8y - 4 = 15y - 6 - 5
8y - 4 = 15y - 11
- 4 + 11 = 15 y - 8y
7 = 7y
7y = 7
y = 7/7
y = 1

g)
2(3 - a) + 7(2 - a) = 15 - 4a
6 - 2a + 14 - 7a = 15 - 4a
20 - 9a = 15 - 4a
20 - 15 = 9a - 4a
5 = 5a
5a = 5
a = 5/5
a = 1

h)
2(x - 2) + 5(2 - x) + 6(x + 1) = 0
2x - 4 + 10 - 5x + 6x + 6 = 0
2x + 6x - 5x - 4 + 6 + 10 = 0
3x + 16 - 4 = 0
3x + 12 = 0
3x = - 12
x = -12/3
x = - 4

i)
2 [x - 2(x + 2)] - 3 = x + 3(x + 1)
2 [x - 2x - 4] - 3 = x + 3x + 3
2[-x - 4] - 3 = 4x + 3
-2x - 8 - 3 = 4x + 3
-2x - 4x = 3 + 8 + 3
-6x = 14
x = -14/6
x = - 7/3

j)
3(y - 3) + 4 = 2[ - (y - 5) - 4 (2y + 1)]
3y - 9 + 4 = 2 [ - y + 5 - 8y - 4]
3y - 5 = 2 [ -9y + 1]
3y - 5 = - 18y + 2
3y + 18y = 2 + 5
21y = 7
y = 7/21
y = 1/3