anonymous one year ago WILL MEDAL AND FAN Solve for x: 3 over 4 x + 5 over 8 = 4x it will be a fraction...

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1. mathstudent55

You mean this? |dw:1433463970632:dw|

2. anonymous

I can't do fractions... I am better at decimals, so thanks for the help!

3. anonymous

first, we isolate the variable, right.. SO we would do something with 5/8

4. mathstudent55

We can do this equation with decimals because the decimals in this case are simple and terminate. If you have a fraction which is a non-terminating decimal, changing fractions into decimals won't be such a good idea, so I think it's better to keep the fractions as fractions and work through them.

5. mathstudent55

Yes, we do want to isolate the variable, so we need all terms with x on the left side.

6. anonymous

would we add 5/8 to the other side?

7. mathstudent55

We also want all simple numbers on the right side. Let's start by moving the 5/8 to the right side.

8. mathstudent55

To decide whether we add 5/8 or subtract 5/8, you need to see what the 5/8 is doing where it is now.

9. mathstudent55

The 5/8 is being added on the left side. The opposite of addition is subtraction, so we subtract 5/8 from both sides.

10. mathstudent55

|dw:1433464376460:dw|

11. mathstudent55

Ok, as you see, we already moved the 5/8 to the right side. Now we want the 4x on the left side.

12. mathstudent55

To do that, we subtract 4x from both sides.

13. mathstudent55

|dw:1433464587100:dw|

14. anonymous

ok... I get it

15. anonymous

kind of

16. mathstudent55

We subtracted 4x from both sides. We are close to the answer. We have just a number on the right side, which is good. We have all terms with x on the left side. Now we need to combine both terms with x on the left side. Since we are dealing with fractions, we need to write 4x as a fraction.

17. anonymous

4/1

18. mathstudent55

Any whole number can be written as a fraction by simply writing the number over 1. For example, 5 = 5/1; x = x/1; 8 = 8/1

19. mathstudent55

Good.

20. mathstudent55

|dw:1433464750480:dw|

21. mathstudent55

To add or subtract fractions, we need a common denominator. We need the LCD (lowest common denominator) between 4 and 1. The LCD of 4 and 1 is 4. The LCD is the smallest number that is divisible by both numbers.

22. mathstudent55

|dw:1433464906174:dw|

23. anonymous

omg the library closes in 4 minutes, do you think we could speed this up? Sorry to sound like a pain, believe me I appreciate any help that I get.

24. mathstudent55

Since we need the fraction 4/1 to have a denominator of 4, and its denominator is now 1, we need to multiply the denominator by 4. That means we need to multiply the numerator also by 4. 4 * 4 = 16, so we get 16/4.

25. mathstudent55

Yes, almost done. I'll go quickly. You can review it later.

26. mathstudent55

We subtract the fractions on the left side. |dw:1433465019576:dw|

27. mathstudent55

Since x is being multiplied by -13/4, we multiply both sides by its reciprocal: -4/13 |dw:1433465084258:dw|

28. mathstudent55

The left side is only x. We multiplty the fractions on the right side and reduce.

29. mathstudent55

|dw:1433465145822:dw|

30. mathstudent55

Ok, gtg. Bye.

31. anonymous

-5/26?

32. anonymous

33. mathstudent55

No, it's positive 5/26 since both fractions on the right side are negative, and negative times negative is positive.

34. mathstudent55

You're welcome.