What is 6/10 e^{-1/2 x}+3/4 >0 ?

The solution to 6/10 e^{-1/2 x}+3/4 >0 is True for all x

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6/10 e^{-1/2 x}+3/4 >0

\frac{6}{10} e^{- \frac{1}{2} x} + \frac{3}{4} > 0

True for all x

Interval Notation

(- \infty, \infty)

Solution steps

\frac{6}{10} e^{- \frac{1}{2} x} + \frac{3}{4} > 0

\frac{6}{10} e^{- \frac{1}{2} x} = \frac{3 e ^{- \frac{1}{2} x}}{5}

\frac{3 e ^{- \frac{1}{2} x}}{5} + \frac{3}{4} > 0

Move

\frac{3}{4}

to the right side

\frac{3 e ^{- \frac{1}{2} x}}{5} > - \frac{3}{4}

Multiply both sides by

5

3 e^{- \frac{1}{2} x} > - \frac{15}{4}

Divide both sides by

3

e^{- \frac{1}{2} x} > - \frac{5}{4}

Apply exponent rules

True for all x

4.03 x^{2} + 2.08 x - 1.04 = 0

12 - x^{2} = x^{2} - 6

2 - 3 ∣ 5 - 6 x ∣ = - 49

100 0^{\frac{- 2}{3}}

∣ 5 x - 2 ∣ = 0

What is 6/10 e^{-1/2 x}+3/4 >0 ?
The solution to 6/10 e^{-1/2 x}+3/4 >0 is True for all x