Six times a number increased by 20 is four less than eight times the number. Find the number

1 answer:

4 0

Greetings!

"Six times a number increased by 20 is four less than eight times the number. Find the number."...

This would be, as an equation:
 $6x+20=8x-4$

Solve:
Add 4 and -6x to both sides.
$(6x+20)+4+(-6x)=(8x-4)+4+(-6x)$
Simplify.
$24=2x$
Divide both sides by 2.
$(24)/2=(2x)/2$
Simplify.
$12=x$
$x=12$

x=12

Hope this helps.
-Benjamin

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$\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ 4p(y- k)=(x- h)^2 \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-5\\ k=7\\ p=-2 \end{cases}\implies 4(-2)[x-(-5)]=[y-7]^2 \\\\\\ -8(x+5)=(y-7)^2\implies x+5=\cfrac{(y-7)^2}{-8}\implies \boxed{x=-\cfrac{1}{8}(y-7)^2-5}$