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

Question

Solve for x                                                                                     

Answer 1

Hi, Devyn.

I read the question as:

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.

 

Answer 2

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.