Solve the following equations and inequalities: 1) −x2+2x>1 2) |1−3x|=5 3) |4x−3|≤2

trefoniu1

trefoniu1

Answered

2022-01-24

Solve the following equations and inequalities:
1) x2+2x>1
2) |13x|=5
3) |4x3|2

Answer & Explanation

terorimaox

terorimaox

Expert

2022-01-25Added 16 answers

a)x2+2x>1
x2+2x1>0
(x22x+1)>0
x22x+1<0
(x1)2<0
Square of any number cannot be negative.Thus, there is no solution.

Aiden Cooper

Aiden Cooper

Expert

2022-01-26Added 14 answers

Consider the part (2):
|13x|=5
±(13x)=5
13x=5
3x=4
x=43
(13x)=5
1+3=5
3x=6
x=2
Hence, the solution is x=43,2
Consider the part (3):
|43x|2
±(43x)2
43x2
3x2
3x2
x23
(43x)2
4+3x2
3x6
x2
Thus, the solution is x=[23,2]

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