What is sqrt(b-7)+6<= 12 ?

The solution to sqrt(b-7)+6<= 12 is 7<= b<= 43

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sqrt(b-7)+6<= 12

b - 7 + 6 \leq 12

7 \leq b \leq 43

Interval Notation

[7, 43]

Solution steps

b - 7 + 6 \leq 12

Move

6

to the right side

b - 7 \leq 6

Square both sides

(b - 7)^{2} \leq 6^{2}

Simplify

b - 7 \leq 36

Move

7

to the right side

b \leq 43

Find singularity points

Find non-negative values for radicals:

b \geq 7

Combine the intervals

b \leq 43 and b \geq 7

Merge Overlapping Intervals

7 \leq b \leq 43

8 w - 21 = 2 w - 9

9 x^{2} + 90 x - 99

x - 4 x^{3}

x^{17}

\frac{6 c ^{2} + 9 c}{3 c}