How do you solve #(x+6)/x=10/7#?

1 Answer
Jan 15, 2017

Answer:

#x=14#

Explanation:

In solving an equation where one fraction is equal to another fraction we can use the method of #color(blue)"cross-multiplication"#

#rArrcolor(blue)(x+6)/color(red)(x)=color(red)(10)/color(blue)(7)#

Now multiply the #color(red)"red terms"# together, the #color(blue)"blue terms"# together and equate them.

#rArrcolor(red)(10x)=color(blue)(7(x+6))#

distribute the bracket.

#rArr10x=7x+42#

subtract 7x from both sides of the equation.

#10x-7x=cancel(7x)cancel(-7x)+42#

#rArr3x=42#

To solve for x, divide both sides by 3

#(cancel(3) x)/cancel(3)=42/3#

#rArrx=14" is the solution"#

#color(blue)"As a check"#

substitute x = 14 into the equation and if the left side equals the right side then x = 14 is the solution.

#"left side " =(14+6)/14=20/14=10/7=" right side"#