Question

solve the equation.

Answer 1

\[\left(\begin{matrix}20 \\ 2x-10\end{matrix}\right)+\left(\begin{matrix}1 \\ x-5\end{matrix}\right)=\left(\begin{matrix}11 \\2\end{matrix}\right)\]

Answer 2

x=7

Answer 3

Find the gcd(greatest common divisor)

Is (2x-10)(x-5)(2) And multiply by that the whole ecuation.

It will cancel the division and it will leave you with.

20(x-5)(2) +(1)(2x-10)(2)=(11)(2x-10)(x-5)

SImplifying

20(2x-10)+(4x-20)=550-220 x+22 x²

This would be.

40x-200+4x-20=550-220x+22x²

44x-220=550-220x+22x²

Sustract both sides 44x and sum both sides 220

22x²-264x+770=0

You have a cuadratic equation, firts divide by 22 the whole equation

x²-12x+35=0

Factorizing will be

(x-7)(x-5)=0

So the answer will be.

x=7
and
x=5

Answer 4

thanks man for showing all the work!