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# 1/4x+x=-3+1/2x

Solve for x

Is it (1/4)x or (1/4x)?

9/27/2012

Hi, Devyn.

1/4 x + x = 3 + 1/2 x

So here is how to work this equation.  You can combine the terms on the left hand side,  1/4 x + x

Remember that a plain x is the same as 1x, so adding them together gives you  1 1/4 x. (That is supposed to be a mixed number, a whole number 1 and the fraction 1/4.)

You can leave that in the improper form,      5/4 x       to make the subtraction easier in the next step.

so you now have:      5/4 x = 3 + 1/2 x

You have to subtract the    1/2 x    from both sides to get all the variables on one side of the equation. To subtract fractions you have to have the same denominator, so we will rewrite    1/2 x      as     2/4 x

5/4 x - 2/4 x = 3 + 2/4 x - 2/4 x

The    + 2/4 x - 2/4 x    cancels out, so you have:

3/4 x = 3

To undo the 3/4 times x, you would divide by 3/4. BUT, remember that when you divide by a fraction, you actually multiply the reciprocal (turn the fraction over). So:  (the asterisk stands for multiplication)

3/4 x * 4/3 = 3 * 4/3

The 3/4 and 4/3 cancel out; on the right you multiply 3/1 by 4/3

x = 12/3      which simplifies to         x = 4

You can check it by substituting 4 back into the original equation:

1/4 * 4 + 4 = 3 + 1/2 * 4

That simplifies to     1 + 4 = 3 + 2      which is true, so our solution works.

The first thing you probably noticed is those pesky x's in the denominator.  To get rid of those, we will want to multiply the entire equation by x:

x(1/(4x)+x)=x(-3+1/(2x))    And distribute the x's through

1/4+x2=-3x+1/2   Now move all of the terms over to the left side of the equation

x2+3x-1/4=0  And now we have a quadratic equation.

Use the quadratic formula to solve for x.  You will have 2 answers for x, and each answer will have a square root which can not be simplified.  You'll know that you have the correct solutions for x if you plug them back in to the original equation, and the right hand side equals the left hand side.

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