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

The solution to -2+sqrt(3x+3)<= 7 is -1<= x<= 26

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

- 2 + 3 x + 3 \leq 7

- 1 \leq x \leq 26

Interval Notation

[- 1, 26]

Solution steps

- 2 + 3 x + 3 \leq 7

Move

2

to the right side

3 x + 3 \leq 9

Square both sides

(3 x + 3)^{2} \leq 9^{2}

Simplify

3 x + 3 \leq 81

3 x + 3 \leq 81 : x \leq 26

x \leq 26

Find singularity points

Find non-negative values for radicals:

x \geq - 1

Combine the intervals

x \leq 26 and x \geq - 1

Merge Overlapping Intervals

- 1 \leq x \leq 26

\frac{1}{a} - \frac{2 a}{a}

2 v^{2} - v - 3

7 x^{2} = - 21

12 8^{\frac{1}{3}} \cdot 4^{\frac{1}{3}}

- \frac{\frac{5}{3}}{( - \frac{1}{8} )}