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2 x + 1 < 5 x < 9 – 6 x

i) 2 x + 1 < 5 x

(2 x + 1) – 1 < 5 x – 1

2 x < 5 x – 1

2 x – 5 x < (5 x – 1) – 5 x

-3 x < - 1

- 3 x / - 3 > - 1 / - 3 (If we multiply both sides by a negative number then the sign will flip.)

x > 1 / 3

ii) 5 x < 9 – 6 x

5 x + 6 x < (9 – 6 x) + 6 x

13 x < 9

13 x / 13 < 9 / 13

x < 9 / 13

Therefore 1/3

i) 5>3x+1

5-1 > 3x+1-1

4 > 3x

4/3 > x

ii) 3x+1 > 4 x + 1

3x+1-4x > 4x + 1 -4x

-x > 1

X < -1