Question 624176
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Hi, there--

The Problem:
You did not say, but I suspect that you want to solve this equation for x.
{{{(3/4)x+1/2=(1/4)x-3/2}}}

Solution:
We want to combine the x terms on the left hand side. Subtract (1/4)x from both sides. 
{{{(3/4)x+1/2-(1/4)x=(1/4)x-3/2-(1/4)x}}}

The terms (3/4)x-(1/4)=(1/2)x. The terms (1/4)x-(1/4)x=0 so you no longer have x terms on 
the right hand side.
{{{(1/2)x+1/2=-3/2}}}

We want to combine the constant terms on the right hand side of the equation. Subtract 1/2 from 
both sides.
{{{(1/2)x+1/2-1/2=-3/2-1/2}}}

The constants 1/2-1/2=0 so we have no constant terms on the left side of the equation.
-3/2-1/2 combines to -4/2, or -2.

{{{(1/2)x=-2}}}

Multiply both sides of the equation by 2 to make the coefficient of the x term be 1 (Note: 1/2
and 2 are reciprocal number, so (1/2)*2 = 1.)
{{{x=-4}}}

It's always a good idea to check your work for errors. Substitute -4 for x in the original equation.
{{{(3/4)x+1/2=(1/4)x-3/2}}}
{{{(3/4)(-4)+1/2=(1/4)(-4)-3/2}}}
{{{-3+1/2=-1-3/2}}}
{{{-2&1/2=-2&1/2}}}
Check!

That's it! We solved for x and found that x = -4 is an equivalent form of the original equation.
Please email me if you have questions or comments about the solution.

Ms.Figgy
math.in.the.vortex@gmail.com
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