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I just need someone to help me work out the answer!
Solve for x: 3(x + 1) = −2(x − 1) − 4.
answer choices: 1 −1 −5 −25
I know you do the parenthesis first, right?
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?
-2x +1 = 3x-5?? I duck at this stuff
lol I meant suck
Let's do it one step at a time. We start with the original equation: |dw:1433462580564:dw|
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.
Oh, the distributive property!
-2x -2 x 1 -4 ??
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.
Now let's do the distributive property on the right side. |dw:1433462795731:dw|
You need to be careful with the signs on the left side.
Now we simplify both sides.
3x+3= -2x +2-4 ??
now, we have to solve it!?
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|
ok I am following you
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|
then you add 3 to both sides? Or do you get rid of x?
I mean subtract
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.
5x = -5
divide both sides by positive 5
to get x= -1 !!??
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.
Thank you so much for your help! Wish me luck....
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.
you fill in the number?
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|
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.
The solution is x = -1. We were correct.
YAYY! Thanks, again.. I gave you a medal and fanned you.
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!
Wait, do you mind helping with one more? I will open new question if you want?!
No problem. Please start a new post. I'll help you there.