SOLUTION: 1/2 (x + 1) - x/3 (2x - 1) = 2/3. Solve for x. Not sure how to solve.

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Question 1205252: 1/2 (x + 1) - x/3 (2x - 1) = 2/3.
Solve for x.
Not sure how to solve.
Found 4 solutions by ikleyn, josgarithmetic, MathTherapy, greenestamps:
Answer by ikleyn(52829) About Me  (Show Source):
You can put this solution on YOUR website!
.

Multiply both sides of the equation by 6.

Combine like terms.

Reduce to the standard quadratic equation form.

Solve the quadratic equation, using the quadratic formula or factoring.


If you are given an assignment to solve a quadratic equation, then it is assumed
that you have the methods of solving it as your pre-requisite knowledge.


If not, learn on how to solve quadratic equations using the quadratic formula from these lessons

    - Introduction into Quadratic Equations
    - PROOF of quadratic formula by completing the square

in this site.



Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
1/2 (x + 1) - x/3 (2x - 1) = 2/3


Your spacings make this look like should be
%281%2F2%29+%28x+%2B+1%29+-+%28x%2F3%29+%282x+-+1%29+=+2%2F3

Multiply both sides by 6, simplify, and solve.


cross%28highlight%28system%281%2F8%2Cor%2C11%2F8%29%29%29

3%28x%2B1%29-2x%282x-1%29=4
3x%2B3-4x%5E2%2B2x=4
-4x%5E2%2B5x=1
4x%5E2-5x%2B1=0

x=%285%2B-+sqrt%2825-16%29%29%2F%282%2A4%29
x=%285%2B-+3%29%2F8
system%28x=1%2F4%2Cor%2Cx=1%29

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
1/2 (x + 1) - x/3 (2x - 1) = 2/3.

Solve for x.

Not sure how to solve.

He's WRONG!! It's NOT highlight%28system%281%2F8%2Cor%2C11%2F8%29%29, so highlight%28cross%28system%281%2F8%2Cor%2C11%2F8%29%29%29

Correct answer: highlight_green%28matrix%281%2C3%2C+highlight%281%2F4%29%2C+or%2C+highlight%281%29%29%29

I wonder who died and made that over-the-hill senior citizen and racist, boss - one who decides what
responses are useful or useless to students. He needs to stop trailing/stalking me, and find something 
productive to do. Apparently, he's bored, probably extremely lonely, need attention, and need to be heard.
You better leave me the H..L ALONE, OLD MAN!

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Another response from know-it-all "tutor" @MathTherapy that is of absolutely no use to the student....

Well, it takes all kinds to make a world.

%281%2F2%29%28x%2B1%29-%28x%2F3%29%282x-1%29=2%2F3

Multiply everything by the least common denominator (6) to clear fractions.

3%28x%2B1%29-%282x%29%282x-1%29=4

Expand, combine like terms, and put in standard form for a quadratic.

3x%2B3-4x%5E2%2B2x=4
4x%5E2-5x%2B1=0

Factor and solve.

%284x-1%29%28x-1%29=0

x=1/4 or x=1

ANSWERS: 1/4, 1