Question

Ecuatii cu modul,va rog am nevoie cat de repede poibil.

Answer 1

Explicație pas cu pas:

1.|2x-3|=5 deci 2x-3=5, 2x=8,x=4 sau 2x-3= -5, 2x= -2, x= -1. x apartine multimii {-1,4}

2.

$\sqrt{(3x + 1) {}^{2} } = |3x + 1| = 7 \\ 3 \times + 1 = 7 \\ 3x = 6 \\ x = 2 \\ 3x + 1 = - 7 \\ 3 x = - 8 \\ x = - \frac{8}{3 }$

x apartine multimii {-8/3, 2}

c) |3x-2|-3=1

|3x-2|=4, deci 3x-2=4, 3x=6,x=2 sau 3x-2= -4,

3x= -2, x= -2/3

d) |3x-2|= |x+8| , 3x-2=x+8, 2x=6, x=3

sau 3x-2=-(x+8), 3x-2= -x-8, 4x=-6, x= -6/4

x= -3/2

x apartine multimii {-3/2, 3}

Answer 2

a) |2x - 3| = 5

2x - 3 = 5 => x = 4

2x - 3 = - 5 => x = - 1

S = {4 ; -1}

b) √[(3x + 1)²] = 7

|3x + 1| = 7

3x + 1 = 7 => x = 2

3x + 1 = - 7 => x = - 8/3

S = {2 ; - 8/3}

c) |3x - 2| - 3 = 1

|3x - 2| = 1 + 3

|3x - 2| = 4

3x - 2 = 4 => x = 2

3x - 2 = - 4 => x = - 2/3

S = {2 ; - 2/3}

d) |3x - 2| = |x + 8|

3x - 2 = x + 8 => x = 5

3x - 2 = - (x + 8) => x = - 3/2

S = {5 ; - 3/2}

e) |x² - 25| + |x + 5| = 0

|x² - 25| = - |x + 5|

{|x² - 25| = 0 => {x = - 5 ; x = 5

{- |x + 5| = 0 => {x = - 5

=> x = - 5