tìm x : x/3=16/24,x/4=16-x
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\(a)x=\dfrac{1}{4}+\dfrac{5}{13}=\dfrac{33}{52}.\\ b)\dfrac{x}{3}=\dfrac{2}{3}+\dfrac{-1}{7}.\\ \Leftrightarrow\dfrac{x}{3}=\dfrac{11}{21}.\\ \Leftrightarrow\dfrac{7x}{21}=\dfrac{11}{21}.\\ \Rightarrow7x=11.\\ \Leftrightarrow x=\dfrac{11}{7}.\\ c)\dfrac{x}{3}=\dfrac{16}{24}+\dfrac{24}{36}=\dfrac{2}{3}+\dfrac{2}{3}=\dfrac{4}{3}.\\ \Rightarrow x=4.\\ d)\dfrac{x}{15}=\dfrac{1}{5}+\dfrac{2}{3}=\dfrac{13}{15}.\\ \Rightarrow x=13.\)
Giải
a) 24 + (15-x) = 16
<=> 15-x=16-24
<=> 15-x=(-8)
<=> x = 15-(-8) => x = 23
b) 11 - (24-x) =
<=> 24-x= 11 - (-27)
<=> 24 - x = 38
<=> x = 24 - 38 => x = -14
c) |x-16| = 42
<=> x-16=42 và x-16=-42
<=> x = 42 + 16 ; x =-42+16
<=> x = 58 ; x = -26
d) 10-2|x| = (-2) . (-3)
<=> 10 - (-2) . (-3) = 2|x|
<=> 10 - 6 = 2|x|
<=> 2|x| = 4
<=> |x| = 4 : 2 = 2
=> x = 2 hoặc x = (-2)
A/ 24+(15-x)=16
(15-x)= 16- 24
(15-x)= - 18
x = 5 - (-18)
x = 23
B/ 11-(24-x)=(-3)3
(24-x)=11- 27
(24-x)= -16
x = 24 -(- 16)
x= 40
C/
\(\left|x-16\right|=42\hept{\begin{cases}x-16=42\\x-16=-42\end{cases}}\hept{\begin{cases}x=42+16\\x=-42+16\end{cases}}\hept{\begin{cases}x=58\\x=-26\end{cases}}\)
D/ 10-2|x|=(-2)x(-3)
10-2|x|=6
2|x|=10-6
2|x|=4
x=4:2
x=2
a)\(\dfrac{4}{x}=\dfrac{x}{16}\)
<=>\(x^2=4.16=64\)
<=>\(x=\pm8\)
<=>x=-8(vì x<0)
b)\(\dfrac{x}{-24}=\dfrac{-6}{x}\)
<=>\(x^2=\left(-24\right)\left(-6\right)=144\)
<=>\(x=\pm12\)
<=>x=12(Vì x>0)
\(B=\frac{1+x^2+x^4+...+x^{26}}{1+x^4+x^8+...+x^{24}}\)
\(=\frac{\frac{\left(x^2-1\right)\left(1+x^2+x^4+...+x^{26}\right)}{x^2-1}}{\frac{\left(x^4-1\right)\left(1+x^4+x^8+...+x^{24}\right)}{x^4-1}}\)
\(=\frac{\frac{x^{28}-1}{x^2-1}}{\frac{x^{28}-1}{x^4-1}}=\frac{x^4-1}{x^2-1}=x^2+1\)
1: \(\Leftrightarrow x=UCLN\left(24;36;150\right)=6\)
2: \(\Leftrightarrow x\in\left\{24;48;72;...\right\}\)
mà 16<=x<=50
nên \(x\in\left\{24;48\right\}\)
3: \(\Leftrightarrow x\inƯ\left(6\right)\)
mà x>-10
nên \(x\in\left\{1;-1;2;-2;3;-3;6;-6\right\}\)
4: \(\Leftrightarrow x\in BC\left(4;5;8\right)\)
\(\Leftrightarrow x\in\left\{...;-40;0;40;80;120;160;200;...\right\}\)
mà -20<x<180
nên \(x\in\left\{0;40;80;120;160\right\}\)
2.
a, x-13=-46
=>x=(-46)+13
=>x=33
b, 4x-6=22
=>4x=22+6
=>4x=28
=>x=28:4
=>x=7
3.
a, 32=25
48=24.3
=>ƯCLN(32,48)=24=16
16=24
72=23.32
=>ƯCLN(16,72)=23=8
b,
24=23.3
60=22.3.5
=>BCNN(24,60)=23.3.5=120
72=23.32
180=22.32.5
=>BCNN(72,180)=23.32.5=360