# Simple fractional equation

• May 4th 2009, 11:44 AM
dreamer09
Simple fractional equation
So here's the equation.

Solve:

$\displaystyle 7 \frac {1}{2}x -\frac {1}{2}x = 3 \frac {3}{4} + 39$

I know x = 12 because of the answer key, but I keep getting the wrong answer. I really need a step-by-step explanation.

thanks
• May 4th 2009, 12:53 PM
masters
Quote:

Originally Posted by dreamer09
So here's the equation.

Solve:

$\displaystyle 7 \frac {1}{2}x -\frac {1}{2}x = 3 \frac {3}{4} + 39$

I know x = 12 because of the answer key, but I keep getting the wrong answer. I really need a step-by-step explanation.

thanks

Hi dreamer09,

You have terms on the left side of your equation with the variable x in them. Combine these. On the right side, you just have numbers. Combine these.

$\displaystyle 7\frac{1}{2}x-\frac{1}{2}x=3 \frac{3}{4}+39$

$\displaystyle 7x=42 \frac{3}{4}$

Now, if you divide $\displaystyle 42 \frac{3}{4}$ by 7, you will not get 12. You will, in fact, get $\displaystyle \frac{171}{28}$. Maybe you miscopied the problem. Check it again.
• May 4th 2009, 01:06 PM
dreamer09
Quote:

Originally Posted by masters
Hi dreamer09,

You have terms on the left side of your equation with the variable x in them. Combine these. On the right side, you just have numbers. Combine these.

$\displaystyle 7\frac{1}{2}x-\frac{1}{2}x=3 \frac{3}{4}+39$

$\displaystyle 7x=42 \frac{3}{4}$

Now, if you divide $\displaystyle 42 \frac{3}{4}$ by 7, you will not get 12. You will, in fact, get $\displaystyle \frac{171}{28}$. Maybe you miscopied the problem. Check it again.

Oh sorry, yes I left something out.

$\displaystyle 7\frac{1}{2}x-\frac{1}{2}x=3 \frac{3}{4}x+39$
• May 4th 2009, 02:03 PM
masters
Quote:

Originally Posted by dreamer09
Oh sorry, yes I left something out.

$\displaystyle 7\frac{1}{2}x-\frac{1}{2}x=3 \frac{3}{4}x+39$

Ok, that's better. Combine the tems on the left side first:

$\displaystyle 7x=3 \frac{3}{4}x+39$

Next, subtract $\displaystyle 3 \frac{3}{4}x$ from both sides of the equation.

$\displaystyle 3 \frac{1}{4}x=39$

Finally divide both sides by $\displaystyle 3 \frac{3}{4}$ to arrive at your desired conclusion.

Now, if it's the arithmetic that's giving you problems, you might want to convert those mixed fractions to improper fractions. Might make it easier to solve.

$\displaystyle 7x=\frac{15}{4}x+39$

Multiply each term by 4.

$\displaystyle 28x=15x+156$

Subtract 15x from both sides

$\displaystyle 13x=156$

Divide by 13.

$\displaystyle x=12$