Question

 

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Answer 1

a: \(x\cdot\left(-6\right)=-66\)

=>\(x\cdot6=66\)

=>\(x=\dfrac{66}{6}=11\)

b: \(-1005\cdot\left(x+2\right)=0\)

=>x+2=0

=>x=-2

c: \(-152-\left(3x+1\right)=\left(-2\right)\cdot\left(-27\right)\)

=>\(-152-\left(3x+1\right)=54\)

=>3x+1=-152-54=-206

=>3x=-206-1=-207

=>\(x=-\dfrac{207}{3}=-69\)

d: \(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+20\right)=20\)

=>\(x+x+1+x+2+...+x+20=20\)

=>\(21x+\left(1+2+3+...+20\right)=20\)

=>\(21x+\dfrac{20\cdot\left(20+1\right)}{2}=20\)

=>\(21x+10\cdot21=20\)

=>\(21x+210=20\)

=>21x=-190

=>\(x=-\dfrac{190}{21}\)