14/2-50/2-25/4+100/5-2/4÷2/6-12/18÷2/4
Answers
Answer:
- 85/12
Step-by-step explanation:
14/2 - 50/2 - 25/4 + 100/5 - (2/4 ÷ 2/6) - (12/18 ÷ 2/4)
- 17/4 - 3/2 - 4/3
= - 85/12
Step-by-step explanation:
Solution−
Given inequation is
\begin{gathered}\rm \: {3}^{x + 2} > {\bigg(\dfrac{1}{9} \bigg) }^{\dfrac{1}{x} } \\ \end{gathered}
3
x+2
>(
9
1
)
x
1
can be rewritten as
\begin{gathered}\rm \: {3}^{x + 2} > {\bigg(\dfrac{1}{ {3}^{2} } \bigg) }^{\dfrac{1}{x} } \\ \end{gathered}
3
x+2
>(
3
2
1
)
x
1
\begin{gathered}\rm \: {3}^{x + 2} > {\bigg( {3}^{ - 2} \bigg) }^{\dfrac{1}{x} } \\ \end{gathered}
3
x+2
>(3
−2
)
x
1
\begin{gathered}\rm \: {3}^{x + 2} > {\bigg(3\bigg) }^{\dfrac{ - 2}{x} } \\ \end{gathered}
3
x+2
>(3)
x
−2
\rm\implies \:x + 2 > - \dfrac{2}{x}⟹x+2>−
x
2
\rm \: x + 2 + \dfrac{2}{x} > 0x+2+
x
2
>0
\rm \: \dfrac{ {x}^{2} + 2x + 2}{x} > 0
x
x
2
+2x+2
>0
Now, x² + 2x + 2 is a quadratic polynomial such that coefficient of x² = 1 > 0 and Discriminant, D = 4 - 8 = - 4 < 0
So, we know, in a quadratic expression ax² + bx + c, if a > 0 and D < 0, then ax² + bx + c > 0
\rm\implies \: {x}^{2} + 2x + 2 > 0⟹x
2
+2x+2>0
Thus,
\rm\implies \:\dfrac{1}{x} > 0⟹
x
1
>0
\rm\implies \:x > 0⟹x>0
\rm\implies \:x \in \: (0, \: \infty )⟹x∈(0,∞)