\(3^x\) - 12 = 15
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\(\frac{3}{3.6.9}+\frac{3}{6.9.12}+\frac{3}{9.12.15}+\frac{3}{12.15.18}=\frac{3}{6}\left(\frac{6}{3.6.9}+\frac{6}{6.9.12}+\frac{6}{9.12.15}+\frac{6}{12.15.18}\right)\)
= \(\frac{1}{2}\left(\frac{1}{3.6}-\frac{1}{6.9}+\frac{1}{6.9}-\frac{1}{9.12}+\frac{1}{9.12}-\frac{1}{12.15}+\frac{1}{12.15}-\frac{1}{15.18}\right)\)
\(=\frac{1}{2}\left(\frac{1}{3.6}-\frac{1}{15.18}\right)=\frac{1}{2}.\frac{14}{270}=\frac{7}{270}\)
a) 42 - x = 5
x = 42 - 5
x = 37
b) 15.(x + 4) = 75
x + 4 = 75 : 15
x + 4 = 5
x = 5 - 4
x = 1
d) x + 18 = 12
x = 12 - 18
x = -6
e) 2x - 15 = -19
2x = (-19) + 15
2x = -4
x = -4 : 2
x = -2
f) 36 : (x^3 - 12) = -3
x^3 - 12 = 36 : (-3)
x^3 - 12 = -12
x^3 = 0
=> x = 0
g)x + 15 = 35
x = 35 - 15
x = 20
h) 2x - 13 = 3^2
2x - 13 = 9
2x = 9 + 13
2x = 22
x = 22 : 2
x = 11
a, \(\dfrac{5\times11\times15\times18}{6\times15\times22\times10}\)
= \(\dfrac{5\times11\times15\times6\times3}{6\times15\times11\times2\times2\times5}\)
= \(\dfrac{5\times11\times15\times6}{5\times11\times15\times6}\) \(\times\) \(\dfrac{3}{2\times2}\)
= 1 \(\times\) \(\dfrac{3}{4}\)
= \(\dfrac{3}{4}\)
b, \(\dfrac{7}{12}\) \(\times\) \(\dfrac{3}{5}\) + \(\dfrac{3}{5}\) \(\times\) \(\dfrac{5}{12}\)
= \(\dfrac{3}{5}\) \(\times\) ( \(\dfrac{7}{12}+\dfrac{5}{12}\))
= \(\dfrac{3}{5}\) \(\times\) \(\dfrac{12}{12}\)
= \(\dfrac{3}{5}\) \(\times\) 1
= \(\dfrac{3}{5}\)
\(\left(15+x\right):3=3^{15}:3^{12}\)
\(\left(15+x\right)=3^3.3\)
\(15+x=3^4\)
\(x=81-15\)
\(x=66\)
\(\left(15+x\right):3=3^{15}:3^{12}\)
\(\left(15+x\right):3=3^{15-12}\)
\(\left(15+x\right):3=3^3\)
\(15+x=3^3.3\)
\(15+x=81\)
\(x=81-15\)
\(x=66\)
\(1,\frac{2}{3}+\frac{4}{9}+\frac{1}{5}+\frac{2}{15}+\frac{3}{2}-\frac{17}{18}\)
\(< =>\frac{4}{9}+\frac{3}{2}+\left(\frac{2}{3}+\frac{1}{5}+\frac{2}{15}\right)-\frac{17}{18}\)
\(< =>\frac{8}{18}+\frac{27}{18}+\left(\frac{10}{15}+\frac{3}{15}+\frac{2}{15}\right)-\frac{17}{18}\)
\(< =>\frac{35}{18}+1-\frac{17}{18}\)
\(< =>\frac{53}{18}-\frac{17}{18}\)
\(< =>2\)
\(2,\frac{13}{28}\cdot\frac{5}{12}-\frac{5}{28}\cdot\frac{1}{12}\)
\(< =>\left(\frac{13}{28}-\frac{5}{28}\right)\cdot\left(\frac{5}{12}-\frac{1}{12}\right)\)
\(< =>\frac{2}{7}\cdot\frac{1}{3}\)
\(< =>\frac{2}{21}\)
\(3,\frac{19}{4}\cdot\frac{15}{23}-\frac{15}{4}\cdot\frac{7}{23}+\frac{15}{4}\cdot\frac{11}{23}\)
\(< =>\frac{285}{92}-\frac{105}{92}+\frac{165}{92}\)
\(< =>\frac{15}{4}\)
b: =>x(8-7)=-33
=>x=-33
c: =>-12x+60+21-7x=5
=>-19x=-76
hay x=4
d: =>-2x-2-x+5+2x=0
=>3-x=0
hay x=3
17 x \(x\) + 15 x \(x\) x 3 + 12 x 15 - \(x\) x 4 = 680
\(x\) x ( 17 + 15 x 3 - 4) + 180 =680
\(x\) x ( 17 + 45 - 4) = 680 - 180
\(x\) x 58 = 500
\(x\) = 500/58
\(x\) = 250/29
17 x \(x\) + 15 x ( \(x\) x 3) + 12 x ( 15 - \(x\) x 4) = 680
17 x \(x\) + 45 x \(x\) + 12 x 15 - 12 x 4 x \(x\) = 680
17 x \(x\) + 45 x \(x\) + 180 - 48 x \(x\) = 680
\(x\) x ( 17 + 45 - 48) + 180 = 680
\(x\) x 14 = 680 - 180
\(x\) x 14 = 500
\(x\) = 500: 14
\(x\) = 250/7
3x - 12 = 15
3x = 27
3x = 33
x = 3
`3^x -12=15`
`3^x=15+12`
`3^x=27`
`3^x = 3^3`
`=> x = 3`