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IceJOKER [234]
3 years ago
5

1. How do the expressions 4(3+x) and (3+3+3+3) + (x+x+x+x) compare to one another?

Mathematics
1 answer:
gladu [14]3 years ago
7 0

Answer:

They are equal

Step-by-step explanation:

4 (3 + x)

= 4 * 3 + 4 * x

= 12 + 4x

(3 + 3 + 3 + 3) + (x + x + x + x)

= 4 * 3 + 4 * x

= 12 + 4x

Therefore, 4(3+x) is equal to (3+3+3+3) + (x+x+x+x).

Hope it helps :)

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so first off, let's simplify both equations, starting off by multiplying both sides by the LCD of all fractions, to do away with the denominators.


\bf \cfrac{10(x-y)-4(1-x)}{3}=y\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{10(x-y)-4(1-x)=3y} \\\\\\ 10x-10y-4+4x=3y\implies \boxed{14x-13y=4} \\\\[-0.35em] ~\dotfill\\\\ 7+x-\cfrac{x-3y}{4}=2x-\cfrac{y+5}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( 7+x-\cfrac{x-3y}{4} \right)=12\left( 2x-\cfrac{y+5}{3} \right)} \\\\\\ 84+12x-3(x-3y)=24x-4(y+5) \\\\\\ 84+12x-3x+9y=24x-4y-20\implies \boxed{-15x+13y=-124}


now, let's do some elimination on those two simplified equations.


\bf \begin{array}{cllcl} 14x&-13y&=&4\\ -15x&+13y&=&-124\\\cline{1-4} -x&&=&-120 \end{array}~\hfill x=\cfrac{-120}{-1}\implies \blacktriangleright x=120 \blacktriangleleft \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{14(120)-13y=4}\implies 1680-13y=4\implies 1680-4=13y \\\\\\ 1676=13y\implies \blacktriangleright \cfrac{1676}{13}=y \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left( 120~,~\frac{1676}{13} \right)~\hfill

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