SOLUTION: Hi all, im struggling to finish off some work at the moment. (There are 3 seperate equations all of the same type). Find x such that 3 - (3/2)x = 8 - 2x is satisfied. Find x s

Algebra ->  Equations -> SOLUTION: Hi all, im struggling to finish off some work at the moment. (There are 3 seperate equations all of the same type). Find x such that 3 - (3/2)x = 8 - 2x is satisfied. Find x s      Log On


   

Question 199592: Hi all, im struggling to finish off some work at the moment. (There are 3 seperate equations all of the same type).
Find x such that 3 - (3/2)x = 8 - 2x is satisfied.
Find x such that 6 - (5/2)x = 12 + 10x is satisfied.
Find x such that 6 + 3x = 18 + 15x is satisfied.
Detailed explantaions of how to solve the previous would be greatly appreciated.
Thnaks, Nick.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

3-%283%2F2%29x=8-2x Start with the given equation.


2%283%29-cross%282%29%28%283%2Fcross%282%29%29x%29=2%288%29-2%282x%29 Multiply EVERY term by the LCD 2 to clear any fractions.


6-3x=16-4x Multiply.


-3x=16-4x-6 Subtract 6 from both sides.


-3x%2B4x=16-6 Add 4x to both sides.


x=16-6 Combine like terms on the left side.


x=10 Combine like terms on the right side.


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

Answer:

So the solution is x=10





# 2

6-%285%2F2%29x=12%2B10x Start with the given equation.


2%286%29-cross%282%29%28%285%2Fcross%282%29%29x%29=2%2812%29%2B2%2810x%29 Multiply EVERY term by the LCD 2 to clear any fractions.


12-5x=24%2B20x Multiply.


-5x=24%2B20x-12 Subtract 12 from both sides.


-5x-20x=24-12 Subtract 20x from both sides.


-25x=24-12 Combine like terms on the left side.


-25x=12 Combine like terms on the right side.


x=%2812%29%2F%28-25%29 Divide both sides by -25 to isolate x.


x=-12%2F25 Reduce.


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

Answer:

So the solution is x=-12%2F25 which in decimal form is x=-0.48.





# 3



6%2B3x=18%2B15x Start with the given equation.


3x=18%2B15x-6 Subtract 6 from both sides.


3x-15x=18-6 Subtract 15x from both sides.


-12x=18-6 Combine like terms on the left side.


-12x=12 Combine like terms on the right side.


x=%2812%29%2F%28-12%29 Divide both sides by -12 to isolate x.


x=-1 Reduce.


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

Answer:

So the solution is x=-1