I С-10. Решение уравнений, сводящихся к линейным 1. Решите уравнение: 1) a) 3x + 7 = 0; б) 13 - 100x = 0; 2) a) 7x-4 = x - 16; б) 13 - 5x = 8 - 2x; в) 4у + 15 = 6y + 17; 3) a) 5x + (3x - 7) = 9; б) Зу – (5 – y) = 11; 4) a) (7x + 1) - (6x + 3) = 5; б) (8x + 11) – 13 = 9x – 5; в) 0,5х + 0,15 = 0; г) 8 -0,8х = 0; г) 1,3р - 11 = 0,8p + 5; д) 0,71х - 13 = 10-0,29x; e) 8c + 0,73 = 4,61 – 8c; в) 48 = 11- (9a + 2); г) 13 - (5х + 11) = 6x; в) 2 = (3x-5) – (7 – 4x); г) 8х + 5 = 119 + (7 – 3x).

Решение:

1) a) 3x + 7 = 0

3x = -7

x = -\\(\frac{7}{3}\)

б) 13 - 100x = 0

-100x = -13

x = \\(\frac{13}{100}\) = 0.13

2) a) 7x - 4 = x - 16

7x - x = -16 + 4

6x = -12

x = -2

б) 13 - 5x = 8 - 2x

-5x + 2x = 8 - 13

-3x = -5

x = \\(\frac{5}{3}\)

в) 4y + 15 = 6y + 17

4y - 6y = 17 - 15

-2y = 2

y = -1

3) a) 5x + (3x - 7) = 9

5x + 3x - 7 = 9

8x = 9 + 7

8x = 16

x = 2

б) 3y - (5 - y) = 11

3y - 5 + y = 11

4y = 11 + 5

4y = 16

y = 4

4) a) (7x + 1) - (6x + 3) = 5

7x + 1 - 6x - 3 = 5

x - 2 = 5

x = 7

б) (8x + 11) - 13 = 9x - 5

8x + 11 - 13 = 9x - 5

8x - 2 = 9x - 5

8x - 9x = -5 + 2

-x = -3

x = 3

в) 0.5x + 0.15 = 0

0.5x = -0.15

x = -\\(\frac{0.15}{0.5}\) = -0.3

г) 8 - 0.8x = 0

-0.8x = -8

x = \\(\frac{-8}{-0.8}\) = 10

г) 1.3p - 11 = 0.8p + 5

1.3p - 0.8p = 5 + 11

0.5p = 16

p = \\(\frac{16}{0.5}\) = 32

д) 0.71x - 13 = 10 - 0.29x

0.71x + 0.29x = 10 + 13

1x = 23

x = 23

e) 8c + 0.73 = 4.61 - 8c

8c + 8c = 4.61 - 0.73

16c = 3.88

c = \\(\frac{3.88}{16}\) = 0.2425

в) 48 = 11 - (9a + 2)

48 = 11 - 9a - 2

48 = 9 - 9a

9a = 9 - 48

9a = -39

a = -\\(\frac{39}{9}\) = -\\(\frac{13}{3}\)

г) 13 - (5x + 11) = 6x

13 - 5x - 11 = 6x

2 - 5x = 6x

-5x - 6x = -2

-11x = -2

x = \\(\frac{2}{11}\)

в) 2 = (3x - 5) - (7 - 4x)

2 = 3x - 5 - 7 + 4x

2 = 7x - 12

7x = 14

x = 2

г) 8x + 5 = 119 + (7 - 3x)

8x + 5 = 119 + 7 - 3x

8x + 3x = 126 - 5

11x = 121

x = 11

Ответ: 1) a) x = -\\(\frac{7}{3}\); б) x = 0.13; 2) a) x = -2; б) x = \\(\frac{5}{3}\); в) y = -1; 3) a) x = 2; б) y = 4; 4) a) x = 7; б) x = 3; в) x = -0.3; г) x = 10; г) p = 32; д) x = 23; e) c = 0.2425; в) a = -\\(\frac{13}{3}\); г) x = \\(\frac{2}{11}\); в) x = 2; г) x = 11

Превосходно! Ты уверенно решаешь линейные уравнения. Продолжай тренироваться, и ты станешь настоящим мастером в алгебре!