Question

1. /3x +5/+2 = /x + 3-x /
2. /-5-2x / + 3x + 1 = /4×-2/
3. / 3x - 1 / - / 2x +1 / = - 2x +7
4. /2x+4 -3 (2x+1) = -3* /x-5/​

Answer 1

Explicație pas cu pas:

1. /3x +5/+2 = /x + 3-x /

$|3x + 5| + 2 = |x + 3 - x| \\ |3x + 5| + 2 = 3 \\ |3x + 5| = 1$

$3x + 5 = - 1 \\ 3x = - 6 = > x = - 2$

$3x + 5 = 1 \\ 3x = - 4 = > x = - \frac{4}{3}$

2. /-5-2x / + 3x + 1 = /4×-2/

$| - 5 - 2x| + 3x + 1 = |4x - 2| \\ < = > |2x + 5| + 3x + 1 = |4x - 2|$

$2x + 5 = 0 \\ 2x = - 5 = > x = - \frac{5}{2}$

$4x - 2 = 0 \\ 4x = 2 = > x = \frac{1}{2}$

$x \in \left( - \infty ; - \frac{5}{2} \right) \\ - (2x + 5) + 3x + 1 = - (4x - 2) \\ - 2x - 5 + 3x + 1 = - 4x + 2 \\ x + 4x = 2 + 4 \\ 5x = 6 = > x = \frac{6}{5} \\ nu \: apartine \: intervalului$

$x \in \left[ - \frac{5}{2} ; \frac{1}{2} \right) \\ 2x + 5 + 3x + 1 = - (4x - 2) \\ 5x + 6 = - 4x + 2 \\ 5x + 4x = 2 - 6 \\ 9x = - 4 = > x = - \frac{4}{9}$

$x \in \left[\frac{1}{2} ; + \infty \right) \\ 2x + 5 + 3x + 1 = 4x - 2 \\ 5x - 4x = - 2 - 6 \\ x = - 8 \\ nu \: apartine \: intervalului$

$= > x = - \frac{4}{9}$

3. / 3x - 1 / - / 2x +1 / = - 2x +7

$|3x - 1| - |2x + 1| = - 2x + 7$

$3x - 1 = 0 = > x = \frac{1}{3}$

$2x + 1 = 0 = > x = - \frac{1}{2}$

$x \in \left( - \infty ; - \frac{1}{2} \right) \\ - (3x - 1) - ( - (2x + 1)) = - 2x + 7 \\ - 3x + 1 + 2x + 1 = - 2x + 7 \\ - x + 2x = 7 - 2 \\ x = 5 \\ nu \: apartine \: intervalului$

$x \in \left[ - \frac{1}{2} ; \frac{1}{3} \right) \\ - (3x - 1) - (2x + 1) = - 2x + 7 \\ - 3x + 1 - 2x - 1 = - 2x + 7 \\ - 5x + 2x = 7 \\ - 3x = 7 = > x = - \frac{7}{3} \\ nu \: apartine \: intervalului$

$x \in \left[\frac{1}{2} ; + \infty \right) \\ 3x - 1 - (2x + 1) = - 2x + 7 \\ 3x - 1 - 2x - 1 = - 2x + 7 \\ x + 2x = 7 + 2 \\ 3x = 9 = > x = 3$

$= > x = 3$

4. /2x+4 -3 (2x+1) = -3* /x-5/