SOLUTION: Solve for x: 3/4 x

SOLUTION: Solve for x: 3/4 x - 1= 1/4 x +11??

Question 203760: Solve for x: 3/4 x - 1= 1/4 x +11??
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Here's two solutions. THe first one will work with the fractions as they were given. The second solution will eliminate the fractions as the first step.

First, get the variable on one side of the equation. Subtract (1/4)x from each side:

Now get the variable term by itself. Add 1 to both sides:

And finally change the soefficient of the vairable to 1 by a) dividing both sides by the coefficient, or b) multiplying both sides by the reciprocal of the coefficient. With a fraction in front of the variable, option (b) is easier:

Often it is difficult to solve equations with fractions. (This one wasn't too bad but others can be much more difficult.) So it can be worth the time to eliminate the fractions from the equations at the start. Then, you won't see fractions again until the very last step.

To eliminate fractions from the start:

Make sure both sides of the equation are simplified.
Find the Lowest Common Denominator (LCD) of all the fractions, on both sides of the equation.
Multiply both sides of the equation by the LCD.

Let's use this on your equation:
1. Simplify both sides. Your equation is already simplified so we can skip this.
2. Find the LCD of all the fractions. This is easy since there are only two fractions and they both have the same denominator. The LCD is 4.
3. Multiply both sides of the equation by the LCD:

Using the Distributive Property to multiply we get:

and our fractions are gone. Now we will solve the equation. Start by getting the variable on one side of the equation by subtracting x from both sides:

Next get the variable term by itself by adding 4 to both sides:

Now change the coefficient of x to a 1. This time, since the coefficient is an integer, we will divide both sides by it:

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