What is sqrt(3-x)<= 1-x ?

The solution to sqrt(3-x)<= 1-x is x<=-1

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sqrt(3-x)<= 1-x

3 - x \leq 1 - x

x \leq - 1

Interval Notation

(- \infty, - 1]

Solution steps

3 - x \leq 1 - x

f (x) \leq g (x)

then

g (x) \geq 0

1 - x \geq 0 : x \leq 1

3 - x \leq 1 - x : x \leq - 1 or x \geq 2

Find singularity points

Find non-negative values for radicals:

x \leq 3

Combine the intervals

x \leq 1 and (x \leq - 1 or x \geq 2) and x \leq 3

Merge Overlapping Intervals

x \leq - 1

Verify Solutions:

x \leq - 1

True

The solution is

x \leq - 1

x + 3 + x + 2 - 2 x + 4 > 0

lo g_{x} (x) < 2

x - 1 > 3 - x

x^{2} - 4 x > x - 2

(x - 8)^{\frac{1}{2}} - (18 - x)^{\frac{1}{2}} > (2)^{\frac{1}{2}}