## anonymous one year ago WILL MEDAL AND FAN, JUST NEED HELP REVIEWING

1. anonymous

I just need someone to help me work out the answer!

2. anonymous

Solve for x: 3(x + 1) = −2(x − 1) − 4.

3. anonymous

answer choices: 1 −1 −5 −25

4. anonymous

I know you do the parenthesis first, right?

5. mathstudent55

Yes. Distribute the 3 on the left side, and distribute the -2 on the right side. That gets rid of the parentheses on both sides. What do you get?

6. anonymous

-2x +1 = 3x-5?? I duck at this stuff

7. anonymous

lol I meant suck

8. mathstudent55

Let's do it one step at a time. We start with the original equation: |dw:1433462580564:dw|

9. mathstudent55

Now we distribute the 3 on the left side. To distribute a number by a quantity in parentheses, we multiply the number outside the parentheses by each term inside the parentheses. Let's do just the left side first.

10. anonymous

Oh, the distributive property!

11. mathstudent55

|dw:1433462685387:dw|

12. anonymous

-2x -2 x 1 -4 ??

13. mathstudent55

Yes, we are using the distributive property of multiplication over addition on the left side. You see, 3(x + 1) turns into 3 * x + 3 * 1. We will simplify that in the next step.

14. mathstudent55

Now let's do the distributive property on the right side. |dw:1433462795731:dw|

15. mathstudent55

You need to be careful with the signs on the left side.

16. mathstudent55

Now we simplify both sides.

17. mathstudent55

|dw:1433462877297:dw|

18. anonymous

3x+3= -2x +2-4 ??

19. mathstudent55

Exactly.

20. anonymous

now, we have to solve it!?

21. mathstudent55

Now we collect like terms on the right side. 2 and -4 are like terms. They both have no variable. We can combine them together. |dw:1433462994203:dw|

22. anonymous

ok I am following you

23. mathstudent55

Since we are solving for x, we want x by itself on the left side and the numbers by themselves on the right side. Let's deal with the terms with x first. We see -2x on the right side. Since the term -2x and the term -2 (both on the right side) are being added together, we add 2x to both sides to move the -2x to the left side. |dw:1433463153571:dw|

24. mathstudent55

Great.

25. anonymous

then you add 3 to both sides? Or do you get rid of x?

26. anonymous

I mean subtract

27. mathstudent55

Subtract is correct. Now we have all terms with x on the left side. Now we need to get all terms that are just numbers on the right side. We see on the left side that 3 is being added to 5x. We want that 3 on the right side, so we subtract 3 from both sides.

28. mathstudent55

|dw:1433463277247:dw|

29. anonymous

5x = -5

30. mathstudent55

Exactly.

31. anonymous

divide both sides by positive 5

32. anonymous

to get x= -1 !!??

33. mathstudent55

We still want the x by itself, but there is a 5 with the x. The 5 is multiplying the x. We do the opposite operation to multiplication which is division. We divide both sides by 5.

34. mathstudent55

|dw:1433463388210:dw|

35. anonymous

Thank you so much for your help! Wish me luck....

36. mathstudent55

One final thing. With many problems, you answer them, and you don;t really know whether the answer is correct or incorrect until your teacher grades your work. With an equation, we can find out by ourselves if x = -1 is really correct or not.

37. anonymous

you fill in the number?

38. mathstudent55

By stating that x = -1, we are saying that if we plug in -1 for x in the equation, the equation will be true. Let's check it for ourselves: In the second line below, I replaced x with our solution, -1. |dw:1433463548144:dw|

39. mathstudent55

Now we work out the math to see if the statement above is true. If it is true, then x = -1 is the correct solution.

40. mathstudent55

|dw:1433463631425:dw|

41. mathstudent55

The solution is x = -1. We were correct.

42. anonymous

YAYY! Thanks, again.. I gave you a medal and fanned you.

43. mathstudent55

Good luck with your studies. If you see me online again and have a question, don't hesitate to ask. It's been great working with you!

44. anonymous

Wait, do you mind helping with one more? I will open new question if you want?!

45. mathstudent55

No problem. Please start a new post. I'll help you there.