Solve the inequalities and equations a)\frac{x-1}{x+2}\geq0 b)\frac{5}{12}-\frac{1}{2x}=\frac{1}{3x} c)\frac{3x-15}{x}\leq5-x d)\frac{3x+4}{x^2}=\frac{2}{x}

David Rojas

David Rojas

Answered question

2022-01-22

Solve the inequalities and equations
a)x1x+20
b)51212x=13x
c)3x15x5x
d)3x+4x2=2x

Answer & Explanation

lilwhitelieyc

lilwhitelieyc

Beginner2022-01-23Added 10 answers

I did the first one
a)x1x+20
x10 and x+2>0
x1 and x2
then x[1,)
or x10 and x+2<0
x1 and x<2
x(,2)
Combining, we get x(,2)[1,)
izumrledk

izumrledk

Beginner2022-01-24Added 15 answers

b)51212x=13x
512=13x+12x
512=2+36x
512=56x
112=16x
6x=12
x=2
c)3x15x5x
We find the critical point of the inequality:
3x15x=5x
3x15=5xx2
x25x+3x15=0
x(x5)+3(x5)=0
(x5)(x+3)=0
x5=0 or x+3=0
x=5 or x=3
x=0 makes left denominator equal to 0. Now, check intervals in between critical points
x3 works in given inequality
3x<0 doesnt

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