solve inequality

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solve inequality

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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im writing info
\[x-4=\sqrt{x+8}\]
x will be equal to 1

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can u show me how plzzzzz! an dthanks
\[(x-4)^2 = x+8\] \[x^2 -8x +16 = x+8\] combine similar terms it will become \[x^2 -9x+8 =0\] factor (x+9) (x-1) = 0 to check, substitute x=-9 or x=1
thanks:)
\(x-4 = \sqrt{x+8}\) First, before ANYTHING else, think about the Domain. \(x+8\ge 0\;or\;x \ge -8\) You tell me why? \(x-4\ge 0\;or\;x \ge 4\) You tell me why? After that, if we get ANY result for x that is less than 4, we will simply discard it as extraneous. It should not even be considered as a solution. x = 1 is not correct. x = -9 is not correct.
yeah thanks:)
Seriously. Go try them in the original equation. They fail miserably.
well then is the answer zero
No, x = 0 is also incorrect. The only suspected results are x = 1 and x = 8. (The factoring shown above was incorrect.) x = 1 is immediately discarded as not in the Domain. x = 8 is a solution. x = -9 could not have been a solutions, as -9 < 1. x = 0 could not be a solution, as 0 < 1 If you rule out ALL your suspects, there is NO solution. In this case x = 8 is the winner.
ohh well thats not one of my answer choices?:/
opps nv thanks for the help

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