Tập nghiệm của phương trình: −8x−10=∣−8x−10∣ là
A.{x \(\in\) R x \(\ge\) _\(\dfrac{5}{4}\)} B.{x \(\in\) R x \(\le\) _\(\dfrac{5}{4}\)}
C.\(\varnothing\) D. {\(-\dfrac{5}{4}\)}
Tập nghiệm của phương trình: −8x−10=∣−8x−10∣ là
A.{x \(\in\) R x \(\ge\) _\(\dfrac{5}{4}\)} B.{x \(\in\) R x \(\le\) _\(\dfrac{5}{4}\)}
C.\(\varnothing\) D. {\(-\dfrac{5}{4}\)}
\(-8x-10=\left|-8x-10\right|\)
\(\left|-8x-10\right|=-8x-10\) khi \(-8x-10\ge0\Leftrightarrow-8x\ge10\Leftrightarrow x\le-\dfrac{5}{4}\)
PT trở thành :
\(-8x-10=-8x-10\)
\(\Leftrightarrow-8x+8x=-10+10\)
\(\Leftrightarrow0x=0\)
PT có vô số nghiệm
Vậy \(S=\){\(x\in R\)| x\(\le-\dfrac{5}{4}\)}
\(\left|-8x-10\right|=-\left(-8x-10\right)=8x+10\) khi \(-8x-10< 0\Leftrightarrow-8x< 10\Leftrightarrow x>-\dfrac{5}{4}\)
PT trở thành :
\(-8x-10=8x+10\)
\(\Leftrightarrow-8x-8x=10+10\)
\(\Leftrightarrow-16x=20\)
\(\Leftrightarrow4x=-5\)
\(\Leftrightarrow x=-\dfrac{5}{4}\)(KTMĐK)
Vậy \(S=\){\(x\in R\)|x \(\le-\dfrac{5}{4}\)}
=> Đáp án B đúng
Giải bất phương trình :
a, \(\sqrt{5x^2+14x+9}-\sqrt{x^2-x-20}\dfrac{< }{ }5\sqrt{x+1}\)
b, \(2x\sqrt{x}+\dfrac{5-4x}{\sqrt{x}}\dfrac{>}{ }\sqrt{x+\dfrac{10}{x}-2}\)
c, \(\sqrt{3x+1}-\sqrt{6-x}+3x^2-14x-8< 0\)
Bài 3. Giải bất phương trình và biểu diễn tập hợp nghiệm trên trục số:
a) \(\dfrac{2x + 2}{5} + \dfrac{3}{10} < \dfrac{3x - 2}{4}\)
b) \(\dfrac{2 + x}{3} < \dfrac{3 + 2x}{5}\)
d) \(1 + \dfrac{3(x + 1)}{10} > \dfrac{x - 2}{5}\)
e) \(\dfrac{2x - 7}{6} \) ≥ \(\dfrac{3x - 7}{2}\)
f) \(\dfrac{2x - 1}{3} > \dfrac{3x + 1}{2}\)
giải phương trình
a)\(\sqrt{x-1}+\sqrt{4x-4}-\sqrt{25x-25}+2=0\)
b)\(\sqrt{16x+16}-\sqrt{9x+9}+\sqrt{4x+4}+\sqrt{x+1}=16\)
c)\(\sqrt{4x+20}+\sqrt{x+5}-\dfrac{1}{3}\sqrt{9x+45}=4\)
d)\(\dfrac{1}{3}\sqrt{2x}-\sqrt{8x}+\sqrt{18x}-10=2\)
a) \(\sqrt{x-1}+\sqrt{4x-4}-\sqrt{25x-25}+2=0\) (ĐK: \(x\ge1\))
\(\Leftrightarrow\sqrt{x-1}+\sqrt{4\left(x-1\right)}-\sqrt{25\left(x-1\right)}+2=0\)
\(\Leftrightarrow\sqrt{x-1}+2\sqrt{x-1}-5\sqrt{x-1}+2=0\)
\(\Leftrightarrow-2\sqrt{x-1}=-2\)
\(\Leftrightarrow\sqrt{x-1}=\dfrac{2}{2}\)
\(\Leftrightarrow\sqrt{x-1}=1\)
\(\Leftrightarrow x-1=1\)
\(\Leftrightarrow x=2\left(tm\right)\)
b) \(\sqrt{16x+16}-\sqrt{9x+9}+\sqrt{4x+4}+\sqrt{x+1}=16\) (ĐK: \(x\ge-1\))
\(\Leftrightarrow\sqrt{16\left(x+1\right)}-\sqrt{9\left(x+1\right)}+\sqrt{4\left(x+1\right)}+\sqrt{x+1}=16\)
\(\Leftrightarrow4\sqrt{x+1}-3\sqrt{x+1}+2\sqrt{x+1}+\sqrt{x+1}=16\)
\(\Leftrightarrow4\sqrt{x+1}=16\)
\(\Leftrightarrow\sqrt{x+1}=4\)
\(\Leftrightarrow x+1=16\)
\(\Leftrightarrow x=15\left(tm\right)\)
bài 3giải các phương trình sau
b,\(\dfrac{2x}{3}=8\)
d,\(\dfrac{6}{5}x=-9\)
f,\(\dfrac{2-3x}{4}=\dfrac{4x-5}{5}\)
h,\(\dfrac{10-3x}{2}=\dfrac{6x+1}{3}\)
Lời giải:
b.
$\frac{2x}{3}=8$
$\Leftrightarrow 2x=3.8=24$
$\Leftrightarrow x=24:2=12$
d.
$\frac{6}{5}x=-9$
$\Leftrightarrow x=-9: \frac{6}{5}=\frac{-15}{2}$
f.
$\frac{2-3x}{4}=\frac{4x-5}{5}$
$\Leftrightarrow 5(2-3x)=4(4x-5)$
$\Leftrightarrow 10-15x=16x-20$
$\Leftrightarrow 30=31x$
$\Leftrightarrow x=\frac{30}{31}$
h.
$\frac{10-3x}{2}=\frac{6x+1}{3}$
$\Leftrightarrow 3(10-3x)=2(6x+1)$
$\Leftrightarrow 30-9x=12x+2$
$\Leftrightarrow 28=21x$
$\Leftrightarrow x=\frac{28}{21}=\frac{4}{3}$
Giải phương trình :
\(\dfrac{x}{10}+\dfrac{x-1}{9}+\dfrac{x-2}{8}+\dfrac{x-3}{7}+\dfrac{x-4}{6}+\dfrac{x-5}{5}\)= 6
\(\frac{x}{10}+\frac{x-1}{9}+\frac{x-2}{8}+\frac{x-3}{7}+\frac{x-4}{6}+\frac{x-5}{5}=6\)
=> \(\left(\frac{x}{10}-1\right)+\left(\frac{x-1}{9}-1\right)+\left(\frac{x-2}{8}-1\right)+\left(\frac{x-3}{7}-1\right)+\left(\frac{x-4}{6}-1\right)+\left(\frac{x-5}{5}-1\right)=0\)
=> \(\frac{x-10}{10}+\frac{x-10}{9}+\frac{x-10}{8}+\frac{x-10}{7}+\frac{x-10}{6}+\frac{x-10}{5}=0\)
=> \(\left(x-10\right)\left(\frac{1}{10}+\frac{1}{9}+\frac{1}{8}+\frac{1}{7}+\frac{1}{6}+\frac{1}{5}\right)=0\)
=> x - 10 = 0
=> x = 10
Giải các phương trình sau: (TM ĐK)
1) \(\dfrac{11}{x}=\dfrac{9}{x+1}+\dfrac{2}{x-4}\)
2) \(\dfrac{14}{3x-12}-\dfrac{2+x}{x-4}=\dfrac{3}{8-2x}-\dfrac{5}{6}\)
3) \(\dfrac{x+5}{x^2-5x}-\dfrac{x+25}{2x^2-50}=\dfrac{x-5}{2x^2+10}\)
4) \(\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}=\dfrac{16}{x^2-1}\)
5) \(\left(1-\dfrac{x-1}{x+1}\right)\left(x+2\right)=\dfrac{x+1}{x-1}+\dfrac{x-1}{x+1}\)
mng giúp mk bài này nha. Cảm ơn bạn nhiều
\(1,\left(dk:x\ne0,-1,4\right)\)
\(\Leftrightarrow\dfrac{9}{x+1}+\dfrac{2}{x-4}-\dfrac{11}{x}=0\)
\(\Leftrightarrow\dfrac{9x\left(x-4\right)+2x\left(x+1\right)-11\left(x+1\right)\left(x-4\right)}{x\left(x+1\right)\left(x-4\right)}=0\)
\(\Leftrightarrow9x^2-36x+2x^2+2x-11x^2+44x-11x+44=0\)
\(\Leftrightarrow-x=-44\)
\(\Leftrightarrow x=44\left(tm\right)\)
\(2,\left(đk:x\ne4\right)\)
\(\Leftrightarrow\dfrac{14}{3\left(x-4\right)}-\dfrac{2+x}{x-4}-\dfrac{3}{2\left(x-4\right)}+\dfrac{5}{6}=0\)
\(\Leftrightarrow\dfrac{14.2-6\left(2+x\right)-3.3+5\left(x-4\right)}{6\left(x-4\right)}=0\)
\(\Leftrightarrow28-12-6x-9+5x-20=0\)
\(\Leftrightarrow-x=13\)
\(\Leftrightarrow x=-13\left(tm\right)\)
giải phương trình sau:
a) \(\dfrac{8}{x-8}+\dfrac{11}{x-11}=\dfrac{9}{x-9}+\dfrac{10}{x-10}\)
b) \(\dfrac{x}{x-3}-\dfrac{x}{x-5}=\dfrac{x}{x-4}-\dfrac{x}{x-6}\)
c) \(\dfrac{4}{x^2-3x+2}-\dfrac{3}{2x^2-6x+1}+1=0\)
d) \(\dfrac{1}{x-1}+\dfrac{2}{x-2}+\dfrac{3}{x-3}=\dfrac{6}{x-6}\)
a/\(\dfrac{8}{x-8}+1+\dfrac{11}{x-11}+1=\dfrac{9}{x-9}+1+\dfrac{10}{x-10}+1\)
=>\(\dfrac{8+x-8}{x-8}+\dfrac{11+x-11}{x-11}=\dfrac{9+x-9}{x-9}+\dfrac{10+x-10}{x-10}\)
=>\(\dfrac{x}{x-8}+\dfrac{x}{x-11}-\dfrac{x}{x-9}-\dfrac{x}{x-10}=0\)
=>x.\(\left(\dfrac{1}{x-8}+\dfrac{1}{x-11}+\dfrac{1}{x-9}+\dfrac{1}{x-10}\right)=0\)
=>x=0
b/\(\dfrac{x}{x-3}-1+\dfrac{x}{x-5}-1=\dfrac{x}{x-4}-1+\dfrac{x}{x-6}-1\)
=>\(\dfrac{x-x+3}{x-3}+\dfrac{x-x+5}{x-5}-\dfrac{x-x+4}{x-4}-\dfrac{x-6+6}{x-6}=0\)
=>\(\dfrac{3}{x-3}+\dfrac{5}{x-5}-\dfrac{4}{x-4}-\dfrac{6}{x-6}=0\)
Đến đây thì bạn giải giống câu a
bài 1 :
a) \(\dfrac{2}{5}+\dfrac{3}{8}=\) b)\(\dfrac{7}{6}-\dfrac{2}{3}=\) c)\(\dfrac{5}{9}\times6\) d)\(\dfrac{8}{5}:\dfrac{4}{7}=\)
bài 2:
a) \(\dfrac{4}{5}+\) x =\(\dfrac{5}{6}\) b)x : \(\dfrac{7}{10}=5\)
bài 3 : hai xe ô tô chở được tất cả 16 tấn 8 tạ hàng . Xe ô tô thứ nhất chở được nhiều hơn xe ô tô thứ hai 2 tấn 6 tạ hàng . Hỏi mỗi xe chở được bao nhiêu tạ hàng
bài 4 :
145 \(\times\) 69 + 22 x 145 +145 x 8 + 145 =
bài 1
a)\(=\dfrac{16}{40}+\dfrac{15}{40}=\dfrac{31}{40}\)
b)\(=\dfrac{7}{6}-\dfrac{4}{6}=\dfrac{3}{6}=\dfrac{1}{2}\)
c)\(=\dfrac{30}{9}=\dfrac{10}{3}\)
d)\(=\dfrac{8}{5}\times\dfrac{7}{4}=\dfrac{56}{20}=\dfrac{14}{5}\)
bài 2
a)\(x=\dfrac{5}{6}-\dfrac{4}{5}=\dfrac{25}{30}-\dfrac{24}{30}=\dfrac{1}{30}\)
b)\(x=5\times\dfrac{10}{7}=\dfrac{50}{7}\)
bài 4 :
145 ×× 69 + 22 x 145 +145 x 8 + 145
\(=145\times\left(69+22+8+1\right)=145\times100=14500\)
bài 1:
a, \(\dfrac{2}{5}+\dfrac{3}{8}=\dfrac{16}{40}+\dfrac{15}{40}=\dfrac{31}{40}\)
b,\(\dfrac{7}{6}-\dfrac{2}{3}=\dfrac{7}{6}-\dfrac{4}{6}=\dfrac{3}{6}=\dfrac{1}{2}\)
c,\(\dfrac{5}{9}x6=\dfrac{5}{9}x\dfrac{6}{1}=\dfrac{30}{9}\)
d,\(\dfrac{8}{5}:\dfrac{4}{7}=\dfrac{8}{5}x\dfrac{7}{4}=\dfrac{14}{5}\)
bài 2 :
\(a,\dfrac{4}{5}+x=\dfrac{5}{6}\)
\(x=\dfrac{5}{6}-\dfrac{4}{5}\)
\(x=\dfrac{1}{30}\)
b, \(x:\dfrac{7}{10}=5\)
\(x\) \(=5x\dfrac{7}{10}\)
\(x\) \(=\dfrac{35}{10}\)
bài 3 :
đổi :16 tấn 8 tạ = 168 tạ
2 tấn 6 tạ = 26 tạ
xe ô tô thứ nhất chở số tạ hàng là:
( 168 + 26 ) : 2= 97 ( tạ)
xe ô tô thứ hai chở số tạ hàng là:
97 - 26 = 71 ( tạ)
đáp số :xe ô tô thứ nhất : 97 tạ thóc
xe ô tô thứ hai : 71 tạ thóc
Giải các phương trình:
a) \(\dfrac{x+2001}{5}+\dfrac{x+1999}{7}+\dfrac{x+1997}{9}+\dfrac{x+1995}{11}=-4;\)
b) \(\dfrac{x-15}{100}+\dfrac{x-10}{105}+\dfrac{x-100}{110}=\dfrac{x-100}{15}+\dfrac{x-105}{10}+\dfrac{x-110}{5}.\)
a: \(\Leftrightarrow\left(\dfrac{x+2001}{5}+1\right)+\left(\dfrac{x+1999}{7}+1\right)+\left(\dfrac{x+1997}{9}+1\right)+\left(\dfrac{x+1995}{11}+1\right)=0\)
=>x+2006=0
=>x=-2006
b: \(\Leftrightarrow\left(\dfrac{x-15}{100}-1\right)+\left(\dfrac{x-10}{105}-1\right)+\left(\dfrac{x-100}{5}-1\right)=\left(\dfrac{x-100}{15}-1\right)+\left(\dfrac{x-105}{10}-1\right)+\left(\dfrac{x-110}{5}-1\right)\)
=>x-105=0
=>x=105