Page 76 - Algebra

So,
x + (x + 7) + 3x ≤ 82 5x ≤ 75
x ≤ 15
Also, 3x ≥ x + 7 + 5 2x ≥ 12
x≥ 6
Therefore, 6 ≤ x ≤ 15
6. 9p + 30 > 57 9p > 57 – 30
9p > 27
p >3
5p + 28 < 53
5p < 53 – 28
5p <25
p <5
So, the value of 3 < p <5
Between 3 and 5, there is only one positive integral, which is 4.
7. 4x–y<7 x + 6y < 13
Add the two inequalities 5x + 5y < 20
x + y< 4
8. |15–3x|>9
15 – 3x > 9 or –(15 – 3x) > 9 6 > 3x or –15 + 3x > 9
2 > x or 3x > 24
x < 2 or x > 8
x < 2 or x > 8
9. Minimum area of the carpet = 14 m × 8 m = 112 m2 The inequality will be A ≥ 112 m2
10. –2 < x + 3 and x + 3 < 18 0 < x + 5 and x < 15
x + 5 > 0 and x <15
x > –5 and x <15
–5 < x < 15
Page 75 of 177
Algebra I & II