Question #15991

1.Solve |3x+2|>=5. Show work and answer in interval notatation pls
2. Solve (2x-3)^2=-4

Expert's answer

1.Solve |3x+2|>=5. Show work and answer in interval notation

|3x+2|>=5& lt;==>

-5>=3x+2>=5& lt;==>

-7>=3x>=3& lt;==>

-7/3>=x>=1& lt;==>

xє(-∞;-7/3]U[1;+∞).

2.

Solve (2x-3)^2=-4

4x^2-12x+9=-4

4x^2-12x+9+4=0

4x^2-12x+13=0

D=144-52*4<0 => this equation has no real roots. However, we can find its complex roots:

x1,1=(12+-sqrt(-64))/8=(12+-8i)/8

x1=3/2+i

x2=3/2-i

|3x+2|>=5& lt;==>

-5>=3x+2>=5& lt;==>

-7>=3x>=3& lt;==>

-7/3>=x>=1& lt;==>

xє(-∞;-7/3]U[1;+∞).

2.

Solve (2x-3)^2=-4

4x^2-12x+9=-4

4x^2-12x+9+4=0

4x^2-12x+13=0

D=144-52*4<0 => this equation has no real roots. However, we can find its complex roots:

x1,1=(12+-sqrt(-64))/8=(12+-8i)/8

x1=3/2+i

x2=3/2-i

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