How do you solve #5/6(12p+4)=-13p+4#?

Question

Ethan Adkins · Accepted Answer

See the entire solution process below:

First, multiply both sides of the equation by #color(red)(6)# to eliminate the fraction and keep the equation balanced: #color(red)(6) xx 5/6(12p + 4) = color(red)(6)(-13p + 4)# #cancel(color(red)(6)) xx 5/color(red)(cancel(color(black)(6)))(12p + 4) = color(red)(6)(-13p + 4)# #5(12p + 4) = color(red)(6)(-13p + 4)# #60p + 20 = -78p + 24# Next add #color(red)(78p)# and subtract #color(blue)(20)# from each side of the equation to isolate the #p# terms while keeping the equation balanced: #60p + 20 + color(red)(78p) - color(blue)(20) = -78p + 24 + color(red)(78p) - color(blue)(20)# #60p + color(red)(78p) + 20 - color(blue)(20) = -78p + color(red)(78p) + 24 - color(blue)(20)# #138p + 0 = 0 + 4# #138p = 4# Now, divide each side of the equation by #color(red)(138)# to solve for #p# while keeping the equation balanced: #(138p)/color(red)(138) = 4/color(red)(138)# #(color(red)(cancel(color(black)(138)))p)/cancel(color(red)(138)) = 2/69# #p = 2/69#

Julia Adams · Answer

undefined To solve the equation $ \frac{5}{6}(12p+4)=-13p+4 $:

1. Distribute $ \frac{5}{6} $ to $ 12p $ and $ 4 $ to get $ \frac{5}{6} \times 12p + \frac{5}{6} \times 4 = -13p + 4 $.
2. Simplify both sides of the equation.
3. Combine like terms.
4. Solve for $ p $.