how can i solve this? what are the rules for solve absolute values

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[native python]

Try splitting this up into cases. Then you just need to solve several quadratic equations.

[frigid spindle]

identify critical points

note that these critical points are x=1

[native python]

That's one of them.

[frigid spindle]

well not rly

[frigid spindle]

you mean x≥1?

[native python]

When dealing with problems containing expressions of the form |f(x)|, you should split the real line into segments, where the points between the segments are the zeroes of f(x).

[frigid spindle]

oh i meant intervals

gyaaaaaaa

mixed up words

like how i accidently said get more friends and that sounded so wrong

the critical points and x=1 and x=-2

can you figure out the 3 intervals? ( i already gave the first one, x≥1 )

[astral garnet]

the intervals are -2 < x < 1?

what u do after?

@native python

@frigid spindle

[frigid spindle]

hi

for each interval, determine the signs of x−1 and x+2, and solve the equation accordingly.

[frigid spindle]

thats one but only partially right

x<−2

−2 ≤ x < 1

x ≥ 1

these are the intervals

[astral garnet]

i undersand that

how i change the equation

[frigid spindle]

so for each interval, determine the signs of x−1 and x+2, and solve the equation accordingly.

[astral garnet]

for each interval

[frigid spindle]

lets start with x<−2

x−1<0 and x+2<0, so ∣x−1∣ = −(x−1) = −x+1, ∣x+2∣ = −(x+2) = −x−2

subbing into the equation (−x+1)(−x−2)=3

then we simplify

x^2+x−2=3 and x^2+x−5=0

find all solutions using the quadratic formula

(hint: 1)

[rare hawk]

@astral garnet

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