Use the equation 1/2(x-3)=1/3x+1 for parts a-c.?

Question

a. How can you eliminate the fraction from each side of the equation to make finding the solution easier?
b. Write a word problem for the equation.
c. Solve the equation. Explain each step and give the meaning of the answer.

Answer 1

a. How can you eliminate the fraction from each side of the equation to make finding the solution easier? Multiply both sides of the equation by 2 and then multiply the result by 3.

b. Write a word problem for the equation.
One half of three less than John's age, is equivalent to one third of his age plus one.

c. Solve the equation. Explain each step and give the meaning of the answer

i. mult by 2 ==> (x-3)=2/3x+2
ii. mult by 3 ==> 3x - 9= 2x + 6
iii. combine terms ==> [3-2]x = 6+9

which is, x = 15

Answer 2

a) Mulitply both sides of the equation by a value that will cancel out all denominators. In this case, it would be 6.

c) Follow my answer to step a). Then combine like terms.

3(x-3) = 2x + 6 {Multiply both sides by 6}
3x - 9 = 2x + 6 {Multiply through the parentheses}
3x - 2x = 6 + 9 {Add 9 to both sides, and subtract 2x from both sides}
x = 15

Answer 3

a. Multiple both sides by 6 .

I will solve it first, then do part b

c. 3(x-3)=2x+6

3x-9=2x+6
x=15

b. I have a certain number of marbles (x). If I subtract 3 and then divide that be 2 I will have the same number is if I had divided by 3 and added one.