a) 3(8a-4) +6а; (6 11c + 5 (8-c); a) 7p - 2 (3p-1); б) - 4 (3а+2)+8; в) 2 (y-1)- 2y + 12; г) 16 + 3 (2 - 3y) + 8y; в) 3- 17a - 11(2а - 3); г) 15-5 (1-a)- 6а. 2. Решить уравнення…
a) 3(8a-4) +6а; (6 11c + 5 (8-c); a) 7p - 2 (3p-1); б) - 4 (3а+2)+8; в) 2 (y-1)- 2y + 12; г) 16 + 3 (2 - 3y) + 8y; в) 3- 17a - 11(2а - 3); г) 15-5 (1-a)- 6а. 2. Решить уравнення a) 3x+1=0; б) 13 - 100х = 0; a) 7x-4=*-16; б) 13- 5x=8-2x; в) 4у + 15 = 6y + 17; 8) อั+(3x- 7) =9; б) Зу - (5-y)=11; a) (7x + 1) -(6x + 3)= 5: б) (8x + 11) - 13 -9x -5; 3. Решить задачу Двое рабочих изготовили 657 деталей, причем пер-ный изготовил на 63 детали больше второго. Сколько деталей изготовил каждый рабочий? Папе и дедушке вместе 111 лет. Сколько лет каж-дому, если пала в 2 раза моложе дедушки? Расстояние между цунктами А и В равно 40 кхг. Из пункта В выехал велосипедист, а из пункта А навстречу ему — автомобилкст. Автомобилист проехал до встречк расстояние, в 4 раза большее, чем велосипедист, На как
Let's solve each part of your problem step by step.
1. Simplifying the Expressions
(a) \( 3(8a-4) + 6a \)
First, distribute the 3:
\[ 3 \cdot 8a - 3 \cdot 4 + 6a = 24a - 12 + 6a = 30a - 12 \]
(b) \( 11c + 5(8-c) \)
Distribute the 5:
\[ 11c + 5 \cdot 8 - 5 \cdot c = 11c + 40 - 5c = 6c + 40 \]
(c) \( 7p - 2(3p-1) \)
Distribute the -2:
\[ 7p - 2 \cdot 3p + 2 \cdot 1 = 7p - 6p + 2 = p + 2 \]
(d) \( -4(3a+2) + 8 \)
Distribute the -4:
\[ -4 \cdot 3a - 4 \cdot 2 + 8 = -12a - 8 + 8 = -12a \]
(e) \( 2(y-1) - 2y + 12 \)
Distribute the 2:
\[ 2y - 2 - 2y + 12 = -2 + 12 = 10 \]
(f) \( 16 + 3(2 - 3y) + 8y \)
Distribute the 3:
\[ 16 + 3 \cdot 2 - 3 \cdot 3y + 8y = 16 + 6 - 9y + 8y = 22 - y \]
(g) \( 3 - 17a - 11(2a - 3) \)
Distribute the -11:
\[ 3 - 17a - 22a + 33 = 3 + 33 - 39a = 36 - 39a \]
(h) \( 15 - 5(1-a) - 6a \)
Distribute the -5:
\[ 15 - 5 + 5a - 6a = 10 - a \]
2. Solving the Equations
(a) \( 3x + 1 = 0 \)
\[ 3x = -1 \implies x = -\frac{1}{3} \]
(b) \( 13 - 100x = 0 \)
\[ 100x = 13 \implies x = \frac{13}{100} \]
(c) \( 7x - 4 = -16 \)
\[ 7x = -12 \implies x = -\frac{12}{7} \]
(d) \( 13 - 5x = 8 - 2x \)
Combine terms:
\[ -5x + 2x = 8 - 13 \implies -3x = -5 \implies x = \frac{5}{3} \]
(e) \( 4y + 15 = 6y + 17 \)
Combine terms:
\[ 4y - 6y = 17 - 15 \implies -2y = 2 \implies y = -1 \]
(f) \( x + (3x - 7) = 9 \)
Combine terms:
\[ 4x - 7 = 9 \implies 4x = 16 \implies x = 4 \]
(g) \( 3y - (5 - y) = 11 \)
Distribute the negative:
\[ 3y - 5 + y = 11 \implies 4y - 5 = 11 \implies 4y = 16 \implies y = 4 \]
(h) \( (7x + 1) - (6x + 3) = 5 \)
Combine terms:
\[ 7x + 1 - 6x - 3 = 5 \implies x - 2 = 5 \implies x = 7 \]
(i) \( (8x + 11) - 13 - 9x - 5 = 0 \)
Combine terms:
\[ 8x - 9x + 11 - 13 - 5 = 0 \implies -x - 7 = 0 \implies x = -7 \]
3. Solving the Word Problems
(a) Work Problem: Let \( x \) be the number of details produced by the second worker. The first worker produces \( x + 63 \).
So,
\[ x + (x + 63) = 657 \implies 2x + 63 = 657 \implies 2x = 594 \implies x = 297 \]
Details produced by each:
- First worker: \( 297 + 63 = 360 \)
- Second worker: \( 297 \)
(b) Age Problem: Let \( x \) be the age of the grandfather. Then the father's age is \( \frac{x}{2} \).
So,
\[ x + \frac{x}{2} = 111 \implies \frac{3x}{2} = 111 \implies 3x = 222 \implies x = 74 \]
Ages:
- Grandfather: 74
- Father: \( \frac{74}{2} = 37 \)
(c) Distance Problem: Let \( d \) be the distance the cyclist travels. Then the car travels a distance of \( 4d \).
The total distance is:
\[ d + 4d = 40 \implies 5d = 40 \implies d = 8 \]
Distances traveled:
- Cyclist: 8 km
- Car: \( 4 \times 8 = 32 \) km
Feel free to ask if you need any further clarification or additional problems!
