TN 11th, Maths Chapter 2, Exercise 2.2
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Subject : Maths
Chapter : 2
Exercise : 2.2
Que 1 :
Solve for " x "
(i) |3-x| < 7
|x| < r
-r < x < r
|3-x|<7
-7 < (3-x) < 7
-7-3 < -x < 7-3
-10 < -x < 4
∴ -4 < x < 10
(ii) |4x-5| ≥ -2
|x-a| ≥ r
(x-a) ≥ -r
|4x-5| ≥ 2
∵ r < 0
x ∈ R
(iii) |3-(3/4)x| ≤ 1/4
|3-(3/4)x| ≤ 1/4
3|1-(1/4)x| ≤ 1/4
|1-(1/4)x| ≤ 1/12
|(4-x)/4| ≤ 1/12
1/4|4-x)| ≤ 1/12
|4-x| ≤ (1/12)(4/1)
|4-x| ≤ 1/3
[-(x-4)] ≤ 1/3 |x-a|≤ r
-1/3 ≤ x-4 ≤ 1/3 -r ≤ x-a ≤ r
(-1/3)+(4) ≤ x ≤ (1/3)+(4)
11/3 ≤ x ≤ 13/3
(iv) |x|-10 < -3
|x|<7
-r < x < r
|x|-10 < -3
|x| < -3+10
|x| < 7
-7 < x < 7
Que 2 :
Solve (1/|2x-1|) < 6 and express the solution using the interval notation.
Solution :
(1/|2x-1|) < 6 |x|> r
|2x-1| < 1/6 x<r; x<r
-1/6> 2x-1 > 1/6 x ∈ (-∞,-r) ⋃ (r,∞)
(-1/6)+1 > 2x-1 > (1/6)+1
5/6 > 2x > 7/6
5/12 > x > 7/12
x ∈ (-∞, 5/12] ∪ [7/12,∞)
←-∞ –––––|––––––|––––– ∞→
(5/12) (7/12)
Que 3 :
Solve -3|x|+5 ≤ -2 and graph solution set in an number line.
Solution :
-3|x|+5 ≤-2
-3|x| ≤ -2-5
-3|x| ≤ -7 |x| ≤ r
|x| ≤ 7/3 -r < x < r
-7/3 ≤ x ≤ 7/3 x ∈ (-∞,-r]⋃[∞,r)
x ∈ (-∞,7/3] ⋃ [7/3,∞)
←-∞ –––––]––––––|––––––[––––– ∞→
-7/3 0 7/3
Que 4 :
Solve 2|x+1|-6≤7 & the graph of solution set in an Number line.
Solution :
2|x+1|-6 ≤ 7
2|x+1|≤ 7+6
2|x+1|≤ 13
|x+1| ≤ 13/2
|x-(-1)|≤ 13/2 |x|≤r
-13/2 ≤ x+1 ≤ 13/2 -r < x < r
-15/2 ≤ x ≤ 11/2
←-∞ –––––|––––––|––––––|––––– ∞→
-15/2 0 11/2
Que 5 :
Solve 1/5|10x - 2| < 1
Solution :
1/5|10x-2| < 1
|10x - 2| < 1(5/1)
10x - 2< 5 or 10x - 2 > -5
If 5 is Positive If 5 is negative
10x < 5+2 10x > -5+2
10x < 7 10x > -3
x < 7/10 x > -3/10
-3/10 < x < 7/10
←-∞ –––––|––––––|––––––|––––– ∞→
-3/10 0 7/10
Que 6 :
Solve |5x – 12| < -2
Solution :
|5x - 12| < -2
5 |x - 12/5| < -2
|x-12/5| < -2/5
-(-2/5) < (x-12/5) < (-2/5)
2/5 < (x -12/5) < -(2/5)
(2/5)+(12/5) < x < (-2/5)+(12/5)
14/5 < x < 10/5
This Is Impossible,
So, it Has no solution.
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