How do you find all real number solutions to #root3(2x+3)-1=0#?

Answer 1

Avery Alexander

#root(3)(2x+ 3) = 1#

#(2x + 3)^(1/3) = 1#

#((2x+ 3)^(1/3))^3 = 1^3#

#2x + 3 = 1#

#2x = -2#

#x = -1#

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Answer 2

Eli Assouline

To find all real number solutions to the equation √3(2x+3)-1=0, we can follow these steps:

Add 1 to both sides of the equation: √3(2x+3) = 1.
Divide both sides of the equation by √3: 2x+3 = 1/√3.
Subtract 3 from both sides of the equation: 2x = 1/√3 - 3.
Simplify the right side of the equation: 2x = (1 - 3√3)/√3.
Divide both sides of the equation by 2: x = (1 - 3√3)/(2√3).

Therefore, the real number solution to the equation √3(2x+3)-1=0 is x = (1 - 3√3)/(2√3).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.