Q:

# How do you set up an equation to solve for x with fractions?

A:

In order to solve for x, you must isolate x on one side of an equation. To separate x from a fractional coefficient, you must cancel that fraction, usually by multiplying its inverse. You should not need a calculator, as this is a simple task that usually takes only a minute or two.

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1. ### Determine and simplify fractions in the equation

When working with algebraic expressions, rewrite all division operations as fractions. Distribute coefficients applied to operations of x, so you can see what fractions are influencing x. For example, if you are given the equation y=(3x-4)/2, you can distribute the1/2 coefficient so the equation reads y=(3/2)*x-2.

2. ### Isolate the x by canceling

First, subtract out any terms on the x-side of the equation that don't contain the x variable. For the equation y=(3/2)*x-2, subtract -2 (or add +2) to both sides, creating y+2=(3/2)*x. To cancel a coefficient, multiply both sides by its inverse or reciprocal. For example, the inverse of 1/2 is 2/1, and (1/2)*(2/1)=1. For the equation y+2=(3/2)*x, you would multiply by the reciprocal of 3/2, which is 2/3. (2/3)*(y+2)=(2/3)*(3/2)*x (2/3)*(y+2)=x

3. ### Simplify and solve for x

Because x is isolated, completing the operations on the other side of the equation will give a value for x, unless the other side of the equation contains a variable. In the case of (2/3)*(y+2)=x, if you are solving for y=0, then x=(2/3)*(0+2)=4/3.

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