18. Solve for : (a)|-x +4]1(b)loz-2| = 8(c)12c + 11 = x + 3

1.	18. Solve for : (a)\|-x +4]1(b)loz-2\| = 8(c)12c + 11 = x + 3
Answer» a) \|4-x\| ≤ 1..... open modulus with both the signs (-1 and +1) => -1≤ 4-x ≤1 so, -5 ≤ -x ≤ -3 => 3≤ x ≤ 5 b) \|5x-2\| = 8.....open modulus with both the signs (-8 and +8) => 5x-2 =8 => 5x=10 ,so x = 5or 5x-2 = -8 => 5x = 6 or x = 6/5 c) \|2x+1\| = x+3 so 2x+1 = x+3 or , x = 2 or 2x+1 = -x-3 => 3x = -4or x = -4/3.

Answer»

a) |4-x| ≤ 1..... open modulus with both the signs (-1 and +1)

=> -1≤ 4-x ≤1 so, -5 ≤ -x ≤ -3 => 3≤ x ≤ 5

b) |5x-2| = 8.....open modulus with both the signs (-8 and +8) => 5x-2 =8 => 5x=10 ,so x = 5or 5x-2 = -8 => 5x = 6 or x = 6/5

c) |2x+1| = x+3 so 2x+1 = x+3 or , x = 2

or 2x+1 = -x-3 => 3x = -4or x = -4/3.

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