Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 576

а) x(x − 3)/6 − x/2 = 0
x(x − 3)/6 − x ⋅ 3/2 ⋅ 3 = 0
x² − 3x − 3x/6 = 0
x² − 6x = 0 x(x − 6) = 0 x₁ = 0 x − 6 = 0 x₂ = 6
б) x(x + 1)/3 + 8 + x/4 = 2
x(x + 1) ⋅ 4/3 ⋅ 4 + (8 + x) ⋅ 3/4 ⋅ 3 = 2
4x² + 4x + 24 + 3x/12 = 2
4x² + 7x + 24/12 = 2 ⋅ 12
4x² + 7x + 24 = 24 4x² + 7x = 24 − 24 4x² + 7x = 0 x(4x + 7) = 0 x₁ = 0 4x + 7 = 0 4x = −7 x = −7 : 4 x₂ = −1,75
в) 2/5x + 9 − x/4 + 9 − x/6 = 341/60
2/5x + 9 − x/4 + 9 − x/6 = 221/60 ⋅ 60
2x ⋅ 12 + (9 − x) ⋅ 15 + (9 − x) ⋅ 10 = 221 24x + 135 − 15x + 90 − 10x = 221 −x = 221 − 225 −x = −4 x = 4
г) 1 + x − 3,5/5 + 1/2 = x/3,5 − 1
1 ⋅ 10/1 ⋅ 10 + (x − 3,5) ⋅ 2/5 ⋅ 2 + 1 ⋅ 5/2 ⋅ 5 = x ⋅ 2/3,5 ⋅ 2 − 1 ⋅ 7/1 ⋅ 7
10 + 2x − 7 + 5/10 = 2x − 7/7 ⋅ 70
(8 + 2x) ⋅ 7 = (2x − 7) ⋅ 10 56 + 14x = 20x − 70 14x − 20x = −70 − 56 −6x = −126 x = −126 : (−6) x = 21