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Answer:
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Answer:
a) z = 0.25
b) x = 13
c) x = 13
d) y ∉ R
Solution:
a) 3(z + 1) + 4(z + 0.3) = 20z + 0.95
=> 3z + 3 + 4z + 1.2 = 20z + 0.95
=> 7z + 3 + 1.2 = 20z + 0.95
=> 7z + 4.2 = 20z + 0.95
=> 7z - 20z = 0.95 - 4.2
=> -13z = -3.25
=> z = 0.25
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b) 4(x+2)/5 = 7 + 5x/13
=> 4(x+2)/5 = 7 + 5x/13
=> 4(x+8)/5 = 7 + 5x/3
=> 13(4x + 8) = 455 + 25x
=> 52x + 104 = 455 + 25x
=> 52 - 25x = 455 - 104
=> 27x = 351
=> x = 351/27
=> x = 13
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c) 9x - 5/7 = 6x + 2/5
=> 9x - 5/7 = 6x + 2/5
=> 5(9x - 5) = 7(6x + 2)
=> 45x - 25 = 42x + 14
=> 45x - 42x = 14 + 15
=> 3x = 39
=> x = 39/3
=> x = 13
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d) (1 - 3y)(4 - y)/(2 - 3y)(1 - y) = 1
=> (1 - 3y)(4 - y)/(2 - 3y)(1 - y) = 1
=> (1 - 3y)×(4 - y)/(2 - 3y)×(1 - y) = 1, y ≠ 2/3 & y ≠ 1.
=> (1 - 3y) × (4y - 1) = (2 - 3y) × (1 - y)
=> 4y - 1 - 12y² + 3y - (2 - 2y - 3y + 3y²) = 0
=> 4y - 1 - 12y² + 3y - 2 + 5y - 3y² = 0
=> 12y - 3 - 15y² = 0
=> -15y² + 12y - 3 = 0
=> 5y² - 4y + 1 = 0
Use quadratic formula,
=> y = 4 ± √16 - 20/10
=> y = 4 ± √-4/10
=> y ∉ R
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