Контрольные задания > 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-у) = 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) 1,3p-11=0,8p+5; д) 0,71х-13-10-0,2 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+(7-32
Вопрос:

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-у) = 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) 1,3p-11=0,8p+5; д) 0,71х-13-10-0,2 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+(7-32

Ответ:

  1. 1) a) $$3x + 7 = 0$$
    $$3x = -7$$
    $$x = \frac{-7}{3}$$
    $$x = -2\frac{1}{3}$$
  2. 1) б) $$13 - 100x = 0$$
    $$-100x = -13$$
    $$x = \frac{-13}{-100}$$
    $$x = 0,13$$
  3. 1) в) $$0,5x + 0,15 = 0$$
    $$0,5x = -0,15$$
    $$x = \frac{-0,15}{0,5}$$
    $$x = -0,3$$
  4. 1) г) $$8 - 0,8x = 0$$
    $$-0,8x = -8$$
    $$x = \frac{-8}{-0,8}$$
    $$x = 10$$
  5. 2) a) $$7x - 4 = x - 16$$
    $$7x - x = -16 + 4$$
    $$6x = -12$$
    $$x = \frac{-12}{6}$$
    $$x = -2$$
  6. 2) б) $$13 - 5x = 8 - 2x$$
    $$-5x + 2x = 8 - 13$$
    $$-3x = -5$$
    $$x = \frac{-5}{-3}$$
    $$x = 1\frac{2}{3}$$
  7. 2) в) $$4y + 15 = 6y + 17$$
    $$4y - 6y = 17 - 15$$
    $$-2y = 2$$
    $$y = \frac{2}{-2}$$
    $$y = -1$$
  8. 2) г) $$1,3p - 11 = 0,8p + 5$$
    $$1,3p - 0,8p = 5 + 11$$
    $$0,5p = 16$$
    $$p = \frac{16}{0,5}$$
    $$p = 32$$
  9. 2) д) $$0,71x - 13 = 10 - 0,2$$
    $$0,71x = 10 - 0,2 + 13$$
    $$0,71x = 22,8$$
    $$x = \frac{22,8}{0,71}$$
    $$x \approx 32,11$$
  10. 2) e) $$8c + 0,73 = 4,61 - 8c$$
    $$8c + 8c = 4,61 - 0,73$$
    $$16c = 3,88$$
    $$c = \frac{3,88}{16}$$
    $$c = 0,2425$$
  11. 3) a) $$5x + (3x - 7) = 9$$
    $$5x + 3x - 7 = 9$$
    $$8x = 9 + 7$$
    $$8x = 16$$
    $$x = \frac{16}{8}$$
    $$x = 2$$
  12. 3) б) $$3y - (5 - y) = 11$$
    $$3y - 5 + y = 11$$
    $$4y = 11 + 5$$
    $$4y = 16$$
    $$y = \frac{16}{4}$$
    $$y = 4$$
  13. 3) в) $$48 = 11 - (9a + 2)$$
    $$48 = 11 - 9a - 2$$
    $$48 = 9 - 9a$$
    $$9a = 9 - 48$$
    $$9a = -39$$
    $$a = \frac{-39}{9}$$
    $$a = -4\frac{1}{3}$$
  14. 3) г) $$13 - (5x + 11) = 6x$$
    $$13 - 5x - 11 = 6x$$
    $$2 - 5x = 6x$$
    $$-5x - 6x = -2$$
    $$-11x = -2$$
    $$x = \frac{-2}{-11}$$
    $$x = \frac{2}{11}$$
  15. 4) a) $$(7x + 1) - (6x + 3) = 5$$
    $$7x + 1 - 6x - 3 = 5$$
    $$x - 2 = 5$$
    $$x = 5 + 2$$
    $$x = 7$$
  16. 4) б) $$(8x + 11) - 13 = 9x - 5$$
    $$8x + 11 - 13 = 9x - 5$$
    $$8x - 2 = 9x - 5$$
    $$8x - 9x = -5 + 2$$
    $$-x = -3$$
    $$x = 3$$
  17. 4) в) $$2 = (3x - 5) - (7 - 4x)$$
    $$2 = 3x - 5 - 7 + 4x$$
    $$2 = 7x - 12$$
    $$7x = 2 + 12$$
    $$7x = 14$$
    $$x = \frac{14}{7}$$
    $$x = 2$$
  18. 4) г) $$8x + 5 = 119 + (7 - 3x)$$
    $$8x + 5 = 119 + 7 - 3x$$
    $$8x + 3x = 126 - 5$$
    $$11x = 121$$
    $$x = \frac{121}{11}$$
    $$x = 11$$
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