$\text{a) |x| - 3 = 2017.}$
$\text{⇒ |x| = 2017 + 3.}$
$\text{⇒ |x| = 2020.}$
$\text{⇒ x = ± 2020.}$
$\text{Vậy x = ± 2020.}$
$\text{b) |x| < 3.}$
$\text{⇒ ±x < 3.}$
$\text{* Nếu x > 0 thì 0 < x < 3.}$
$\text{⇒ x ∈ {1; 2}.}$
$\text{* Nếu x < 0 thì x < 0 < 3.}$
$\text{⇒ x ∈ {-1; -2; -3;...}.}$
$\text{c) |3x| - 42 = -15 - |-5|.}$
$\text{⇒ |3x| - 42 = -15 - 5.}$
$\text{⇒ |3x| - 42 = -20.}$
$\text{⇒ |3x| = -20 + 42.}$
$\text{⇒ |3x| = 22.}$
$\text{⇒ 3x = 22 hoặc 3x = -22.}$
$\text{* 3x = 22.}$
$\text{⇒ x = $\dfrac{22}{3}$ ≈ 7,3}$
$\text{* 3x = -22.}$
$\text{⇒ x = $\dfrac{-22}{3}$ ≈ -7,3}$
$\text{Mà x ∈ Z nên x không thỏa mãn đề bài.}$
$\text{Vậy x không thỏa mãn đề bài. :)}$
$\text{d) 25 - 5.|x| = -95.}$
$\text{⇒ 5.|x| = 25 - (-95).}$
$\text{⇒ 5.|x| = 25 + 95.}$
$\text{⇒ 5.|x| = 120.}$
$\text{⇒ |x| = 120 ÷ 5.}$
$\text{⇒ |x| = 24.}$
$\text{⇒ x = ± 24.}$
$\text{Vậy x = ± 24.}$
$\text{e) 4x - 4 = 60.}$
$\text{⇒ 4x = 60 + 4.}$
$\text{⇒ 4x = 64.}$
$\text{⇒ x = 64 ÷ 4.}$
$\text{⇒ x = 16.}$
$\text{Vậy x = 16.}$
$\text{f) $3^{2x}$ + (-1) = 80.}$
$\text{⇒ $3^{2x}$ = 80 - (-1).}$
$\text{⇒ $3^{2x}$ = 80 + 1.}$
$\text{⇒ $3^{2x}$ = 81.}$
$\text{⇒ $3^{2x}$ = $3^{4}$.}$
$\text{⇒ 2x = 4.}$
$\text{⇒ x = 2.}$
$\text{Vậy x = 2.}$
$\text{h) $|-4|^{x+1}$ = 256.}$
$\text{⇒ $4^{x+1}$ = 256.}$
$\text{⇒ $4^{x+1}$ = $4^{4}$.}$
$\text{⇒ x + 1 = 4.}$
$\text{⇒ x = 4 - 1.}$
$\text{⇒ x = 3.}$
$\text{Vậy x = 3.}$
$\text{g) $(2x+1)^{4}$ - $2^{3}$.$(-4)^{2}$ = -50 - (-5).}$
$\text{⇒ $(2x+1)^{4}$ - $2^{3}$.$(-4)^{2}$ = -50 + 5.}$
$\text{⇒ $(2x+1)^{4}$ - $2^{3}$.$(-4)^{2}$ = -45.}$
$\text{⇒ $(2x+1)^{4}$ - 8.16 = -45.}$
$\text{⇒ $(2x+1)^{4}$ - 128 = -45.}$
$\text{⇒ $(2x+1)^{4}$ = -45 + 128.}$
$\text{⇒ $(2x+1)^{4}$ = 83.}$
$\text{Cái này đề sai rồi, em xem lại đề nhé!}$
