Đáp án:
a.$ x=\dfrac{49}{108}$
b.$x=\pm\dfrac23$
c.$x=-\dfrac{10}9$
d.$x=-1.5$
e.$x=\dfrac{21}8$
f.$x=0$
g.$x=-\dfrac92$
h.$x=-\dfrac1{20}$
i.$x=-\dfrac{12}{19}$
k.$x=\dfrac73$
Giải thích các bước giải:
a.Ta có:
$x-\dfrac34=-(\dfrac23)^3$
$\to x-\dfrac34=-\dfrac{8}{27}$
$\to x=\dfrac34-\dfrac8{27}$
$\to x=\dfrac{49}{108}$
b.Ta có:
$2-x^2=\dfrac{14}9$
$\to x^2=2-\dfrac{14}9$
$\to x^2=\dfrac49$
$\to x^2=(\dfrac23)^2$
$\to x=\pm\dfrac23$
c.Ta có:
$x+(-\dfrac13)^2=(-1)^{2021}$
$\to x+\dfrac19=-1$
$\to x=-1-\dfrac19$
$\to x=-\dfrac{10}9$
d.Ta có:
$\dfrac13x-2021^0=-1.5$
$\to \dfrac13x-1=-1.5$
$\to \dfrac13x=1-1.5$
$\to \dfrac13x=-0.5$
$\to x=-1.5$
e.Ta có:
$3x+(x-\dfrac12)=10$
$\to 3x+x-\dfrac12=10$
$\to 4x-\dfrac12=10$
$\to 4x=\dfrac12+10$
$\to 4x=\dfrac{21}2$
$\to x=\dfrac{21}8$
f.Ta có:
$-\dfrac25x+9-(3-x)=6$
$\to -\dfrac25x+9-3+x=6$
$\to -\dfrac25x+6+x=6$
$\to -\dfrac25x+x=0$
$\to x(-\dfrac25+1)=0$
$\to x\cdot \dfrac35=0$
$\to x=0$
g.Ta có:
$-2(x+3)+7=10$
$\to -2(x+3)=3$
$\to x+3=-\dfrac32$
$\to x=-\dfrac32-3$
$\to x=-\dfrac92$
h.Ta có:
$1-x=\dfrac34-6x$
$\to 6x-x=\dfrac34-1$
$\to 5x=-\dfrac14$
$\to x=-\dfrac1{20}$
i.Ta có:
$7x+3(x+2)=\dfrac12x$
$\to 7x+3x+6=\dfrac12x$
$\to 10x+6=\dfrac12x$
$\to 10x-\dfrac12x=-6$
$\to \dfrac{19}2x=-6$
$\to x=-\dfrac{12}{19}$
k.Ta có:
$-x-\dfrac12(x+5)=-6$
$\to -x-\dfrac12x-\dfrac52=-6$
$\to -\dfrac32x-\dfrac52=-6$
$\to -\dfrac32x=\dfrac52-6$
$\to -\dfrac32x=-\dfrac72$
$\to x=\dfrac73$
