Whether the statement “The equation (x+1)2=9 is equivalent to x+1=±3" is true or false.

Square Root Property: If x2=k then x=±k The solution set is {k,−k} or more concisely {±k}. Here, (x+1)2=9 Then, x+12=±9 =±32 =±3 Therefore, the statement “The equation (x+1)2=9 is equivalent to x+1=±3"istrue,

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High School
Algebra
Pre-Algebra
Equations, expressions, and inequalitie

parthe0o

Answered question

2021-11-11

Whether the statement “The equation

{(x + 1)}^{2} = 9

is equivalent to

x + 1 = \pm 3

" is true or false.

Answer & Explanation

Jick1984

Beginner2021-11-12Added 12 answers

Square Root Property:

I f x^{2} = k

then

x = \pm \sqrt{k}

The solution set is

{\sqrt{k,} - \sqrt{k}}

or more concisely

{\pm \sqrt{k}}

.
Here,

{(x + 1)}^{2} = 9

Then,

x + 1^{2} = \pm \sqrt{9}

= \pm \sqrt{3^{2}}

= \pm 3

Therefore, the statement “The equation

{(x + 1)}^{2} = 9

is equivalent to

x + 1 = \pm 3

"istrue,

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