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2 years ago

1/6(x-5)=1/2(x+6) help

Mathematics

1 answer:

anygoal [31]2 years ago

7 0

Answer: x= -23/2

Step-by-step explanation:

multiply both sides of the equation by 6

x-5=3(x+6)

distribute 3

x-5=3x+18

move variables to lest-hand side and change sign

x-3x=18+5

like terms

-2x=23

the divide both sides by -2

x= -23/2

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$\hbox{Domain:}\\
x^2+x-2\geq0 \wedge x^2-4x+3\geq0 \wedge x^2-1\geq0\\
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$
\sqrt{x^2+x-2}+\sqrt{x^2-4x+3}=\sqrt{x^2-1}\\
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(x+2)(x-3)(x-1)^2=\left(\dfrac{-x(x-1)+2(x-1)}{2}\right)^2\\
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(x+2)(x-3)(x-1)^2=\dfrac{(x-2)^2(x-1)^2}{4}\\
4(x+2)(x-3)(x-1)^2=(x-2)^2(x-1)^2\\$
$
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(x-1)^2(4x^2-4x-24-x^2+4x-4)=0\\
(x-1)^2(3x^2-28)=0\\
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x=1 \vee 3x^2=28\\
x=1 \vee x^2=\dfrac{28}{3}\\
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There's one more condition I forgot about
$-(x-2)(x-1)\geq0\\
x\in\langle1,2\rangle\\$

Finally
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\boxed{\boxed{x=1}}$

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