What is sqrt(x-3)<= 7 ?

The solution to sqrt(x-3)<= 7 is 3<= x<= 52

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sqrt(x-3)<= 7

x - 3 \leq 7

3 \leq x \leq 52

Interval Notation

[3, 52]

Solution steps

x - 3 \leq 7

Square both sides

(x - 3)^{2} \leq 7^{2}

Simplify

x - 3 \leq 49

Move

3

to the right side

x \leq 52

Find singularity points

Find non-negative values for radicals:

x \geq 3

Combine the intervals

x \leq 52 and x \geq 3

Merge Overlapping Intervals

3 \leq x \leq 52

\frac{k - 5}{2} = 2

(2 x + 5) (2 x - 5) = 11

30 x^{3} + 22 x^{2} + 4 x

t^{2} - 5 t - 36

X - 4 < \frac{2 X}{3} + \frac{2 - 3 X}{5}