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Popular >

1-x<e^x

Solution

1 - x < e^{x}

Solution

x > 0

+1

Interval Notation

(0, \infty)

Solution steps

1 - x < e^{x}

Switch sides

e^{x} > 1 - x

Prepare

e^{x} > 1 - x

for Lambert form:

1 > (1 - x) e^{- x}

Rewrite the equation with

- x + 1 = u

and

x = - u + 1

1 > (1 - (- u + 1)) e^{- (- u + 1)}

Simplify

1 > e^{u - 1} u

Rewrite

1 > e^{u - 1} u

in Lambert form:

e^{u} u < e

Solve

e^{u} u < e : u < 1

u < 1

Substitute back

- x + 1 = u,

solve for

x

Solve

- x + 1 < 1 : x > 0

x > 0

Popular Examples

10^{3x-1}>10000

1 0^{3 x - 1} > 10000

((12)^x)^2+4x-3>= 9

((12)^{x})^{2} + 4 x - 3 \geq 9

1 + e^{x} > 0

(0.3)^{2x^2-3x-6}<0.00243

(0.3)^{2 x^{2} - 3 x - 6} < 0.00243

4^{x} < 2^{x} + 1 + 3

Frequently Asked Questions (FAQ)

What is 1-x<e^x ?
The solution to 1-x<e^x is x>0