SOLUTION: Solve the linear equation, give its solution set, and state whether the equation is conditional, identity, or inconsistent. 1/2(p+5)-4 = 1/3(2p-1)

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve the linear equation, give its solution set, and state whether the equation is conditional, identity, or inconsistent. 1/2(p+5)-4 = 1/3(2p-1)      Log On


   

Question 126659: Solve the linear equation, give its solution set, and state whether the equation is conditional, identity, or inconsistent.
1/2(p+5)-4 = 1/3(2p-1)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%281%2F2%29%28p%2B5%29-4=%281%2F3%29%282p-1%29 Start with the given equation



%286%29%28%281%2F2%29%28p%2B5%29-4%29=%286%29%28%281%2F3%29%282p-1%29%29 Multiply both sides by the LCM of 6. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



3%28p%2B5%29-24=2%282p-1%29 Distribute and multiply the LCM to each side



3p%2B15-24=4p-2 Distribute


3p-9=4p-2 Combine like terms on the left side


3p=4p-2%2B9Add 9 to both sides


3p-4p=-2%2B9 Subtract 4p from both sides


-p=-2%2B9 Combine like terms on the left side


-p=7 Combine like terms on the right side


p=%287%29%2F%28-1%29 Divide both sides by -1 to isolate p



p=-7 Divide

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Answer:
So our answer is p=-7




Since we get only one answer, the equation is conditional. In other words, the equation is only true if p=-7.