What is 10-sqrt(2x+7)<= 3 ?

The solution to 10-sqrt(2x+7) = 21

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10-sqrt(2x+7)<= 3

10 - 2 x + 7 \leq 3

x \geq 21

Interval Notation

[21, \infty)

Solution steps

10 - 2 x + 7 \leq 3

Move

10

to the right side

- 2 x + 7 \leq - 7

Multiply both sides by

- 1

2 x + 7 \geq 7

Square both sides

(2 x + 7)^{2} \geq 7^{2}

Simplify

2 x + 7 \geq 49

2 x + 7 \geq 49 : x \geq 21

x \geq 21

Find singularity points

Find non-negative values for radicals:

x \geq - \frac{7}{2}

Combine the intervals

x \geq 21 and x \geq - \frac{7}{2}

Merge Overlapping Intervals

x \geq 21

12 x + 8 = 44 - 6 x

2 x^{2} - (x - 2) (x + 5) = 7 (x + 3)

lo g_{2} (64)

- \frac{9}{5} x = - 45

(2 x + 5) (x + 1) = - 1