a) x+3 = 7
x = 7-3
x = 4
b) 5x-4 = 26
5x = 26+4
5x = 30
x = 30:5
x = 6
c) 7x+3 = 4x+6
7x-4x = 6-3
3x = 3
x = 3:3
x = 1
[tex]d) \frac{3}{4}x+\frac{1}{2} = \frac{4}{3}x+\frac{1}{5}|60\\[/tex]
45x+30 = 80x+12
45x-80x = 12-30
-35x = -18
[tex]x=+\frac{18}{35}[/tex]
e) x²+7x-6 = 0
Δ=7²-4*1*(-6) = 73
[tex]x_{1} = \frac{-7+\sqrt{73} }{2}[/tex]
[tex]x_{2} =\frac{-7-\sqrt{73} }{2}[/tex]
f) 3x²+2x-5 = 0
3x²+5x-3x-5 = 0
x(3x+5) - (3x+5) = 0
(x-1)(3x+5) = 0
x-1 = 0 => x = 1
3x+5 = 0 [tex]=> x = -\frac{5}{3}[/tex]
g) 7x²+2x-5 = 3x²+5x-4
7x²-3x²+2x-5x-5+4=0
4x²-3x+1 = 0
4x²+x-4x-1 = 0
x(4x+1) - (4x+1) = 0
(x-1)(4x+1) = 0
x-1 = 0 => x=1
4x+1 = 0 => [tex]x=-\frac{1}{4}[/tex]
h) x²-x+1 = 0
Δ = (-1)²-4*1*1 = 1-4 = -3 < 0 => x∉|R
i) 4x²-4x+1 = 0 <=> (2x-1)² = 0
=> [tex]x_{1,2} = \frac{1}{2}[/tex]
