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

2 Answers
May 21, 2018

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

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}