2 years ago

Solution of inequality -2/5x-9<9/10

1 answer:

5 0

$- \frac{2}{5}x-9\ \textless \ \frac{9}{10} \\(- \frac{2}{5}x-9\ \textless \ \frac{9}{10} )*10 \\ -4x-90\ \textless \ 9 \\ -4x\ \textless \ 9+90 \\ x\ \textgreater \ -\frac{99}{4}$

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Ln a+3 + ln a-3 = ln 16

Lilit [14]

$\bf log_{{ a}}(xy)\implies log_{{ a}}(x)+log_{{ a}}(y)\\\\
and\qquad \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\\\
-----------------------------\\\\
ln(a+3)+ln(a-3)=ln(16)\implies ln[(a+3)(a-3)]=ln(16)
\\\\\\
ln[a^2-3^2]=ln(16)\impliedby \textit{removing ln() from both sides}
\\\\\\
a^2-9=16\implies a^2=16+9\implies a^2=25
\\\\\\
a=\pm\sqrt{25}\implies a=\pm 5$