How do you solve #(5x-10)/(7x+6)=10/8#?

Question

Eli Assouline · Accepted Answer

I got #x = -14/3#. I would first multiply by #8#, and then by #7x+6#. #(5x - 10)/(7x + 6) = 10/8# #(8*(5x - 10))/(7x + 6) = 10/cancel(8)*cancel(8)# #(8(5x - 10))/cancel((7x + 6))*cancel((7x + 6)) = 10*(7x + 6)# From here, just distribute the terms, move the same types of terms to each side, and solve for #x#. #ul(8)(ul(color(red)(5))x - ul(color(darkblue)(10))) = ul(10)(ul(color(red)(7))x + ul(color(darkblue)(6)))# #color(red)(40)x - color(darkblue)(80) = color(red)(70)x + color(darkblue)(60)# #-140 = 30x# #color(blue)(x) = -140/30# #= color(blue)(-14/3)# And we can prove that this is correct: #(5(-14/3) - 10)/(7(-14/3) + 6) stackrel(?" ")(=) 10/8# #(-70/3 - 30/3)/(-98/3 + 18/3) stackrel(?" ")(=) 10/8# #(-100/3)/(-80/3) stackrel(?" ")(=) 10/8# #color(red)(cancel(color(black)(-)))100/color(red)(cancel(color(black)(3)))*color(red)(cancel(color(black)(-)))color(red)(cancel(color(black)(3)))/80 stackrel(?" ")(=) 10/8# #100/80 = color(green)(10/8 = 10/8)#

Savannah Anderson · Answer

undefined To solve the equation $\frac{5x - 10}{7x + 6} = \frac{10}{8}$, follow these steps:

1. Cross multiply to eliminate the fractions:
   $8(5x - 10) = 10(7x + 6)$

2. Distribute and simplify both sides:
   $40x - 80 = 70x + 60$

3. Rearrange the equation to isolate the variable:
   $40x - 70x = 60 + 80$
   $-30x = 140$

4. Divide both sides by $-30$ to solve for $x$:
   $x = -\frac{140}{30}$

5. Simplify the fraction:
   $x = -\frac{14}{3}$

So, the solution to the equation is $x = -\frac{14}{3}$.