Page 47 - Algebra 1

5. Let the length of the shortest piece be x cm Length of the second piece = (x + 7) cm Length of the third piece = 3x
So,
x + (x + 7) + 3x ≤ 82 5x ≤ 75
x ≤ 15
Also, 3x ≥ x + 7 + 5 2x ≥ 12
x≥6
Therefore, ≤ 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. Minimumareaofthecarpet=14m×8m=112m2 The inequality will be A ≥ 112 m2
10. –2<x+3andx+3<18
0 < x + 5 and x < 15 x + 5 > 0 and x <15 x > –5 and x <15 –5 < x < 15
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ALGEBRA