Question

помогите решить
$|1 - 3x| + 4 \times |3 + x| = 12$

​

Answer 1

Ответ:

$x_1 = -3\dfrac{2}{7} ~ ~; ~~ x_2 = -1$

Объяснение:

$|1-3x| + 4|x+3|= 12$

$1 -3x = 0 ~~~~ ; ~~~~ 3+x =0 \\\\ x =\dfrac{1}{3} ~~~~~~~~~~;~~~~ x = -3$

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    +                            +                           —                  1 - 3x

    —                           +                            +                  x + 3

$\hspace{-1,4em}\text{I} )~~ |1-3x| +4\cdot |x+3| = 12 \\\\ 1 -3x -4 (x+3) = 12 \\\\ -7x = 23 \\\\ x _1= -3\dfrac{2}{7} ~ \checkmark ~ ~ , ~ x \in (- \infty ~ ; ~ -3 )$

$\hspace{-1,6em}\text{II} )~~ |1-3x| +4\cdot |x+3| = 12 \\\\ 1 -3x +4 (x+3) = 12 \\\\ x+13 = 12 \\\\ x_2 = -1 ~ \checkmark ~ ~ , ~ x \in [-3 ~ ; ~ 1/3 )$

$\hspace{-1,9em}\text{III} )~~ |1-3x| +4\cdot |x+3| = 12 \\\\ -(1 -3x) +4 (x+3) = 12 \\\\ 7x+11 = 12 \\\\ x_2 = \dfrac{1}{7} ~ \varnothing ~ ~ , ~ x \in [ 1/3 ~; ~ \infty )$