Exercise Problem and Solution Part: 3 (Equation, Solving Equations, Systems of liner equations, Quadratic equations, Inequalities)

Question: 15 If 3X + 5Y = 14 and X - Y = 6, then what is the average of X & Y?

Explore:
3X + 5Y = 14...................(1)
X - Y = 6 ........................(2)
Or, 5X -5Y = 30 ..............(3)

(1) + (2) => 8X = 44

=> X = (44/8) = 5.5
From equation (2), X -Y = 6
=> Y = X - 6 = 5.5 - 6 = -0.5

:. Average of X & Y = (X + Y)/ 2
= (5.5 +(- .5))/ 2
= 2.5
Answer: 2.5

Question: 16 If 6 - 4X ≤ 14, then 
Option: (a) X ≤ 2 (b) X ≥ 2 (c) X ≤ -2 (d) X ≥ - 2 (e) X > - 2
 Explore: 
6 - 4X ≤ 14
=> -4X ≤ 14 - 6
=> -4X ≤ 8
=> X ≥ 8
=> X ≥ -2 [Dividing both sides by (- 4)]
Answer: (d)


Question: 17 If 2X - 4 < 4, then 
Option: (a) X > 2 (b) X < 2 (c) 2 < X < 4 (d) X < 4 (e) 2 > X > 4
Explore: 
     2X - 4 < 4
=> 2X < 4 + 4
=> 2X < 8
=> X < 4
Answer: (d)


Question: 18 If -3t + 8 > t - 6, then
Option: (a) t > 1 (b) t > (7/2) (c) t < 7/2 (d) t < -(7/2) (e) t > - (7/2)
Explore: 
- 3t + 8 > t - 6
Or, 8 + 6 > t + 3 t
Or , 14 > 4t
Or, t < 14/4
Or, t < 7/2
Answer: (c)

Question: 19 If 4X - 7 < 2X + 13, then which of the following must be true?
Option: (a) X <7 (b) X <13 (c) X > 9 (d) None
Explore:
     4X - 7 < 2X + 13
=> 4X -2X < 13 + 7
=> 2X < 20
=> X < 20/2
=> X < 10
Answer: (d)

Question: 20 If 3 - 2X  ≤ 7, then- 
Option: (a) X ≤ 2 (b) X ≥ 2 (c) X ≤ -2 (d) x ≥ -2 (e) x > -2
Explore: 
    3- 2X ≤ 7
=> 3 ≤ 7 + 2X
=> 7 + 2X  ≥ 3
=> 2X ≥ 3 - 7
=> 2X ≥ - 4
=> X ≥ -2
Answer: (d)

Question: 21 If b < 2 and 2X -3b = 0, which of the following must be true?
Option: (a) x > - 3 (b) X < 2 (c) X < 3 (d) None
Explore:
     2X -3b = 0
=> 2X = 3b => 2X/3 = b => 2X/3 < 2
=> x< (2x3)/2 [:. b < 2]
=> X < 3
Answer: (c)

Question: 22 If mx + ny = 12my, then x/y + n/m = ?
Option: (a) 12 (b) 12mn (c) 12m + 12y  (d) 0
Explore:
mx + ny = 12 my
Now x/y + n/m
=(mx + ny)/my
=12my/my
= 12
Answer: (a)

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