SOLUTION: How do i answer these questions? I am trying to help my daughter and can't remember. 2(x+4)+3x=12 On the next one, I can't remember if add the opposite would be add positi

Algebra ->  Equations -> SOLUTION: How do i answer these questions? I am trying to help my daughter and can't remember. 2(x+4)+3x=12 On the next one, I can't remember if add the opposite would be add positi      Log On


   

Question 198874: How do i answer these questions? I am trying to help my daughter and can't remember.
2(x+4)+3x=12


On the next one, I can't remember if add the opposite would be add positive 5 to negative 17, yielding 12 or if it would be add -5 yielding -22
3/4x-5=-17



How do I answer?
2(m-3)=5(2m-6)



When do you need to reverse the inequality sign when you solve an inequality?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

2%28x%2B4%29%2B3x=12 Start with the given equation.


2x%2B8%2B3x=12 Distribute.


5x%2B8=12 Combine like terms on the left side.


5x=12-8 Subtract 8 from both sides.


5x=4 Combine like terms on the right side.


x=%284%29%2F%285%29 Divide both sides by 5 to isolate x.


----------------------------------------------------------------------

Answer:

So the solution is x=4%2F5 which in decimal form is x=0.8.





# 2


%283%2F4%29x-5=-17 Start with the given equation.


4%28%283%2Fcross%284%29%29x%29-4%285%29=4%28-17%29 Multiply EVERY term by the LCD 4 to clear any fractions.


3x-20=-68 Distribute and multiply.


3x=-68%2B20 Add 20 to both sides.


3x=-48 Combine like terms on the right side.


x=%28-48%29%2F%283%29 Divide both sides by 3 to isolate x.


x=-16 Reduce.


----------------------------------------------------------------------

Answer:

So the solution is x=-16




# 3


2%28m-3%29=5%282m-6%29 Start with the given equation.


2m-6=10m-30 Distribute.


2m=10m-30%2B6 Add 6 to both sides.


2m-10m=-30%2B6 Subtract 10m from both sides.


-8m=-30%2B6 Combine like terms on the left side.


-8m=-24 Combine like terms on the right side.


m=%28-24%29%2F%28-8%29 Divide both sides by -8 to isolate m.


m=3 Reduce.


----------------------------------------------------------------------

Answer:

So the solution is m=3





When do you need to reverse the inequality sign when you solve an inequality?

Let's show why by example:


Let's say we have the inequality 1+%3C+10 (which is true; 1 is less than 10). Now divide both sides by a negative number (say -1) to get

%281%29%2F%28-1%29+%3C+%2810%29%2F%28-1%29


-1+%3C+-10


which is now false (-1 is NOT less than -10). So to correct this, we simply flip the inequality sign to get: -1%3E-10 and now the inequality is true again.