3/4 x - 1/6 = 2/3

Answer 1

Hello Malak,

So, what you are being asked to do here is to solve an equation that has fractions in it, as you can see. So, let's treat the equation as normal and just solve by using the laws for adding fractions and dividing.

3/4 x - 1/6 = 2/3

3/4 x = 2/3 + 1/6 <-----To add these fractions we first seek the common denominator, okay?

3/4 x = 4/6 + 1/6 <-----You can see the common denominator was six, right. Now add the fractions.

3/4 x = 5/6 <-----Now we need to divide both sides of the equation by 3/4. Remember we use the reciprocal of the fraction or inverse and multiply when dividing. Therefore:

3/4 x = 5/6

x = 5/6 * 4/3

x = 20/18 or 1 2/18 or 1 1/9

Now, we must check our work, right? We can do this by substituting 1 1/9 for x in the original equation.

3/4 (10/9) - 1/6 = 2/3

30/36 - 1/6 = 2/3 <-----We need to find the least common denominator to subtract the right side.

30/36 - 6/36 = 2/3 <-----Once we found the least common denominator we simply subtracted

24/36 = 2/3 <------24/36 reduces to 2/3

2/3 = 2/3

The solution checks out and is therefore valid. I hope I provided you some assistance with this solution and wish you a great Holiday season. Should you wish to leave feedback, ask further questions regarding this solution, or just want to seek clarity, please click the add comment prompt and leave your commentary which will appear beneath this solution. If you need one-on-one tutoring, please feel free to reach out to me. Best!