Question

Solving an inequality
x-7 lessthan or equal to square root of (x-5)

Answer 1

sorry I am using my ipad unable to use equation editor and I don't know latex

Answer 2

\[ x-7 \le \sqrt{x-5 } \]
start by squaring both sides

Answer 3

yes and I got
x^2-14x+49 > x-5 sorry can't not able to type in greater than or equal to

Answer 4

x^2-15x+54>0

Answer 5

originally you has less than or equal. which is it ?

Answer 6

I know the solution is x> 0 sorry meant greater than

Answer 7

do I factor that or and by the way
I meant the solution is x >9

Answer 8

yes factor

Answer 9

sorry I am on my ipad not my computer
am I suppose to factor the quadratic?

Answer 10

factor
x^2-15x+54>= 0

Answer 11

how does x>6 play into the solution? I mean x>9 would include that interval

Answer 12

you get
(x-6)(x-9) > 0
if you think A*B>0
that means both A and B are positive or both A and B are negative.
so x>6 and x>9 (at the same time)
or
x<6 and x<9 (at the same time) ** this solution gives negative square roots so ignore it

for the first solution, for x to be bigger than 6 and bigger than 9 means just x>=9

Answer 13

to review:
(x-6) * (x-9) will be a negative number if x is (for example) 7: (7-6) * (7-9)= 1 * -2 = -2
and we want
(x-6) * (x-9) >0
so if we need both x>6 and x>9, that simplifies to x>9

Answer 14

thanks