Sure, here are the paraphrased questions: 1. Solve the equation: 1) 9x 8 = 4x + 12; 2) 9 7(x + 3) = 5
1. Solve the equation:
1) 9x 8 = 4x + 12;
2) 9 7(x + 3) = 5 4x.
2. In the first box, there were 5 times more apples than in the second one. When 7 kg of apples were taken from the first box, and 5 kg were added to the second one, the boxes had an equal amount of apples. How many kilograms of apples were in each box initially?
3. Solve the equation:
1) (8y 12)(2.1 + 0.3y) = 0;
2) 7x (4x + 3) = 3x + 2.
4. The first store received 100 kg of candies, and the second one received 240 kg. The first store sold 12 kg of candies daily, and the second one sold 46 kg. In how many days will the second store have 4 times fewer candies left than the first store?
5. For what value of «a» does the equation (a + 3)x = 12:
1) have a root equal to 6;
2) have no roots?
Control work #1 on the topic «Linear Equation with One Variable»
Variant 2
1. Solve the equation:
1) 6x + 15 = 4x + 11;
2) 6 8(x + 2) = 3 2x.
2. Initially, there were 3 times more students in the soccer section than in the basketball section. When 9 more students joined the soccer section, and 33 students joined the basketball section, the sections had an equal number of students. How many students were in each section initially?
3. Solve the equation:
1) (12y + 30)(1.4 + 0.7y) = 0;
2) 9x(5x — 4) = 4x + 4.
4. The first worker had to produce 95 parts, and the second one had to produce 60 parts. The first worker produced 7 parts daily, and the second one produced 6 parts. In how many days will the first worker have to produce twice as many parts as the second worker?
5. For what value of «a» does the equation (a^2)x = 35:
1) have a root equal to 5;
2) have no roots?
Объяснение: Решение уравнений — это процесс нахождения неизвестных переменных, которые удовлетворяют заданному равенству. Для решения уравнений применяются различные методы, такие как упрощение выражений, применение свойств равенств, перенос членов уравнения и решение полученных уравнений.
Пример использования:
1) Дано уравнение: 9x — 8 = 4x + 12
Шаг 1: Перенесем все переменные на одну сторону, получим 9x — 4x = 12 + 8
Шаг 2: Упростим выражение, 5x = 20
Шаг 3: Разделим обе части уравнения на 5, получим x = 4
Ответ: x = 4
2) Дано уравнение: 9 * 7(x + 3) = 5 * 4x
Шаг 1: Упростим обе стороны уравнения, получим 63(x + 3) = 20x
Шаг 2: Раскроем скобки, получим 63x + 189 = 20x
Шаг 3: Перенесем переменные на одну сторону, получим 63x — 20x = -189
Шаг 4: Упростим выражение, получим 43x = -189
Шаг 5: Разделим обе части уравнения на 43, получим x = -189/43
Ответ: x = -189/43
Совет: Для решения уравнений важно использовать правильные шаги и методы решения, а также аккуратность при работе с математическими выражениями. Проверка ответа путем подстановки найденного значения переменной в исходное уравнение может помочь в уверенности в правильности решения.
Упражнение: Решите уравнение: (8y — 12)(2.1 + 0.3y) = 0.