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МатематикаВопрос:
3. Решение уравнений со скобками
Ответ:
Решение уравнений со скобками
- \( 4(x - 6) = x - 9 \)
\( 4x - 24 = x - 9 \)
\( 4x - x = -9 + 24 \)
\( 3x = 15 \)
\( x = 5 \) - \( 6 - 3(x + 1) = 7 - x \)
\( 6 - 3x - 3 = 7 - x \)
\( 3 - 3x = 7 - x \)
\( -3x + x = 7 - 3 \)
\( -2x = 4 \)
\( x = -2 \) - \( (8x + 3) - (10x + 6) = 9 \)
\( 8x + 3 - 10x - 6 = 9 \)
\( -2x - 3 = 9 \)
\( -2x = 12 \)
\( x = -6 \) - \( 14x - 14 = 7(2x - 3) + 7 \)
\( 14x - 14 = 14x - 21 + 7 \)
\( 14x - 14 = 14x - 14 \)
\( 0 = 0 \)
\( x \) — любое число - \( 3(x - 2) = x + 2 \)
\( 3x - 6 = x + 2 \)
\( 3x - x = 2 + 6 \)
\( 2x = 8 \)
\( x = 4 \) - \( 5 - 2(x - 1) = 4 - x \)
\( 5 - 2x + 2 = 4 - x \)
\( 7 - 2x = 4 - x \)
\( -2x + x = 4 - 7 \)
\( -x = -3 \)
\( x = 3 \) - \( (7x+1)-(9x + 3) = 5 \)
\( 7x + 1 - 9x - 3 = 5 \)
\( -2x - 2 = 5 \)
\( -2x = 7 \)
\( x = -3.5 \) - \( 3,4 + 2y = 7(y – 2,3) \)
\( 3.4 + 2y = 7y - 16.1 \)
\( 2y - 7y = -16.1 - 3.4 \)
\( -5y = -19.5 \)
\( y = 3.9 \) - \( 4(5x + 2) = 10(3x - 3) + 15 \)
\( 20x + 8 = 30x - 30 + 15 \)
\( 20x + 8 = 30x - 15 \)
\( 8 + 15 = 30x - 20x \)
\( 23 = 10x \)
\( x = 2.3 \) - \( 2(7x - 7) = 7(2x - 3) + 7 \)
\( 14x - 14 = 14x - 21 + 7 \)
\( 14x - 14 = 14x - 14 \)
\( 0 = 0 \)
\( x \) — любое число - \( 5,6 – 3(2 – 0,4x) = 0,4(4x - 1) \)
\( 5.6 - 6 + 1.2x = 1.6x - 0.4 \)
\( -0.4 + 1.2x = 1.6x - 0.4 \)
\( 1.2x - 1.6x = -0.4 + 0.4 \)
\( -0.4x = 0 \)
\( x = 0 \) - \( 5(x - 12) = 6(x - 10) – x \)
\( 5x - 60 = 6x - 60 - x \)
\( 5x - 60 = 5x - 60 \)
\( 0 = 0 \)
\( x \) — любое число - \( 0,3(8 - 3y) = 3,2 – 0,8(y - 7) \)
\( 2.4 - 0.9y = 3.2 - 0.8y + 5.6 \)
\( 2.4 - 0.9y = 8.8 - 0.8y \)
\( -0.9y + 0.8y = 8.8 - 2.4 \)
\( -0.1y = 6.4 \)
\( y = -64 \) - \( 4(x - 1) = 2(2x - 8) + 12 \)
\( 4x - 4 = 4x - 16 + 12 \)
\( 4x - 4 = 4x - 4 \)
\( 0 = 0 \)
\( x \) — любое число - \( 8(5 – 3x) = 6(2 - 4x) + 7 \)
\( 40 - 24x = 12 - 24x + 7 \)
\( 40 - 24x = 19 - 24x \)
\( 40 = 19 \)
— нет решений - \( 7(4x - 1) = 6 - 2(3 – 14x) \)
\( 28x - 7 = 6 - 6 + 28x \)
\( 28x - 7 = 28x \)
\( -7 = 0 \)
— нет решений - \( 4 - 6(x + 2) = 3 – 5x \)
\( 4 - 6x - 12 = 3 - 5x \)
\( -8 - 6x = 3 - 5x \)
\( -6x + 5x = 3 + 8 \)
\( -x = 11 \)
\( x = -11 \) - \( (5x + 8) – (8x + 14) = 9 \)
\( 5x + 8 - 8x - 14 = 9 \)
\( -3x - 6 = 9 \)
\( -3x = 15 \)
\( x = -5 \) - \( -7(x + 3) + 9 = 5 - 6x \)
\( -7x - 21 + 9 = 5 - 6x \)
\( -7x - 12 = 5 - 6x \)
\( -7x + 6x = 5 + 12 \)
\( -x = 17 \)
\( x = -17 \) - \( –(11x - 7) + (7x + 9) = 8 \)
\( -11x + 7 + 7x + 9 = 8 \)
\( -4x + 16 = 8 \)
\( -4x = 8 - 16 \)
\( -4x = -8 \)
\( x = 2 \)
Ответ: 1) x = 5; 2) x = -2; 3) x = -6; 4) x — любое число; 5) x = 4; 6) x = 3; 7) x = -3.5; 8) y = 3.9; 9) x = 2.3; 10) x — любое число; 11) x = 0; 12) x — любое число; 13) y = -64; 14) x — любое число; 15) нет решений; 16) нет решений; 17) x = -11; 18) x = -5; 19) x = -17; 20) x = 2.
