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(b) s = 6 [1] 5. –x < 8 – 9x 8 – 9x < x
8x < 8 8 < 10x
3 Equations, Inequalities and Graphs x < 1 x > 4
5
4 < x < 1
1. 5x – 6 = 10 – x 5 [2]
6x = 16 6. |3x + 2| . 7 – 2x
x = 8 3x + 2 , –(7 – 2x) 3x + 2 . 7 – 2x
3
x , –9 5x . 5
5x – 6 = –(10 – x) x . 1
4x = –4 [2]
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x = –1
2
2
[2] 7. (x – 5) . 1 1 x + 2
2
3
2. 8 = 28 1 4
2
2
x + 4 x – 1 x – 10x + 25 . x + x + 4
9
3
8x – 8 = 28x + 112 8 x – 34 x + 21 . 0
2
20x = –120 9 3
x = –6 8x – 102x + 189 . 0
2
8 = –28 (4x – 9)(2x – 21) . 0
9
x + 4 x – 1 x , and x . 21
8x – 8 = –28x – 112 4 2 [3]
36x = –104
x = – 26 8. |2 – x| < 3|2x + 4| – 5
9 [2] 2 – x < 3|2x + 4| – 5
7 – x < 3|2x + 4|
3. |x – 3| = 2 + |x + 1| 7 – x < |2x + 4|
x – 3 = 2 + |x + 1| 3 7 – x
|x + 1| = x – 5 2x + 4 > 3
x + 1 = x – 5 x + 1 = –x + 5 6x + 12 > 7 – x
0 = –6 (false) 2x = 4 7x > –5
x = 2 (rejected) 5
x – 3 = –2 – |x + 1| x > – 7
|x + 1| = 1 – x
x + 1 = 1 – x x + 1 = x – 1 2x + 4 > x – 7
2x = 0 0 = –2 (false) 3
x = 0 6x + 12 > x – 7
5x > –19
[4] 19
x > –
1
4. |1 – 2x| = |3x – 24| 5
6 2 – x < 5 – 3|2x + 4|
1
1 – 2x = (3x – 24) –3 – x < –3|2x + 4|
6 3 + x
6 – 12x = 3x – 24 |2x + 4| > 3
x = 2 3 + x
1 2x + 4 > 3
1 – 2x = – (3x – 24)
6 6x + 12 > 3 + x
–6 + 12x = 3x – 24 5x > –9
9
x = –2 x > – (rejected)
When x = 2, 5
y = |1 – 2(2)| 2x + 4 > 3 + x
y = 3 –3
–6x – 12 > 3 + x
When x = –2, –15 > 7x
y = |1 – 2(–2)| x < – 15 (rejected)
y = 5 7
5
[4] The solution is x > – or x < – 19 .
7 5 [3]

Answers 171

Answers Add Math.indd 171 14/03/2022 12:29 PM