How do you solve and check your solutions to #8/5x=4/15#?

2 Answers
May 21, 2018

Answer:

See a solution process below:

Explanation:

Multiply each side of the equation by #color(red)(5)/color(blue)(8)# to solve for #x# while keeping the equation balanced:

#color(red)(5)/color(blue)(8) xx 8/5x = color(red)(5)/color(blue)(8) xx 4/15#

#cancel(color(red)(5))/cancel(color(blue)(8)) xx color(blue)(cancel(color(black)(8)))/color(red)(cancel(color(black)(5)))x = (cancel(color(red)(5))color(red)(1))/(cancel(color(blue)(8))color(blue)(2)) xx (color(blue)(cancel(color(black)(4)))1)/(color(red)(cancel(color(black)(15)))3)#

#x = color(red)(1)/color(blue)(2) xx 1/3#

#x = 1/6#

To check the solution substitute #1/6# for #x# in the original equation and ensure both sides of the equation are equal:

#8/5x = 4/15# becomes:

#8/5 xx 1/6 = 4/15#

#(8 xx 1)/(5 xx 6) = 4/15#

#8/30 = 4/15#

#(2 xx 4)/(2 xx 15) = 4/15#

#(color(red)(cancel(color(black)(2))) xx 4)/(color(red)(cancel(color(black)(2))) xx 15) = 4/15#

#4/15 = 4/15#

May 21, 2018

Answer:

Solution: #\frac{1}{6}#

Check: see below.

Explanation:

Any equation of the form

#ax=b#

yields the solution

#x = b/a#

In your case, #a = 8/5# and #b = 4/15#

So, we must divide by #a#, which is a fraction. So, #b/a# is the same thing as #b \cdot a^{-1}#, where #a^{-1}# is the inverse fraction of #a#, obtained by switching numerator and denominator. So, the solution is

#x = b/a = \frac{4/15}{8/5} = \frac{cancel(4)}{cancel(15)3}\cdot\frac{cancel(5)}{cancel(8)2} = 1/6#

To check the value, simply plug it in, substituting #x#:

#\frac{8}{5}\color(green)(x) = \frac{4}{15} \implies \frac{cancel(8)4}{5}\color(green)(\frac{1}{cancel(6)3}) = \frac{4}{15}#

which is true, since the left hand side evaluates to #\frac{4}{15}#