Question

I'm finding this one difficult. 3/2(x-1) - x+2|3 = 1 - x +11|6

the part with x + 11 |6 means x+11 divided by 6 same with x+2|3 means x+2 divided by 3, I didnt know how to write that. Can someone please show me the steps to this it would be greatly appreciated ! :)

Answer 1

You asked for it.

Answer 2

(3)/(2)*(x-1)-x+(2)/(3)=1-x+(11)/(6)

To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 3. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
(3(x-1))/(2)-x*(3)/(3)+(2)/(3)=1-x+(11)/(6)

Complete the multiplication to produce a denominator of 3 in each expression.
(3(x-1))/(2)-(3x)/(3)+(2)/(3)=1-x+(11)/(6)

Combine the numerators of all expressions that have common denominators.
(3(x-1))/(2)+(-3x+2)/(3)=1-x+(11)/(6)

Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 6. The (3(x-1))/(2) expression needs to be multiplied by ((3))/((3)) to make the denominator 6. The ((-3x+2))/(3) expression needs to be multiplied by ((2))/((2)) to make the denominator 6.
(3(x-1))/(2)*(3)/(3)+(-3x+2)/(3)*(2)/(2)=1-x+(11)/(6)

Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 6.
(3(x-1)(3))/(6)+(-3x+2)/(3)*(2)/(2)=1-x+(11)/(6)

Multiply 3*3 to get 9 in the numerator.
((9)(x-1))/(6)+(-3x+2)/(3)*(2)/(2)=1-x+(11)/(6)

Remove the single term factors from the expression.
(9(x-1))/(6)+(-3x+2)/(3)*(2)/(2)=1-x+(11)/(6)

Multiply 9 by each term inside the parentheses.
(9x-9)/(6)+(-3x+2)/(3)*(2)/(2)=1-x+(11)/(6)

Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 6.
(9x-9)/(6)+((-3x+2)(2))/(6)=1-x+(11)/(6)

Remove the parentheses in the numerator and move the single term to the front of the expression.
(9x-9)/(6)+(2(-3x+2))/(6)=1-x+(11)/(6)

Multiply 2 by each term inside the parentheses.
(9x-9)/(6)+(-6x+4)/(6)=1-x+(11)/(6)

The numerators of expressions that have equal denominators can be combined. In this case, ((9x-9))/(6) and ((-6x+4))/(6) have the same denominator of 6, so the numerators can be combined.
((9x-9)+(-6x+4))/(6)=1-x+(11)/(6)

Simplify the numerator of the expression.
(9x-9-6x+4)/(6)=1-x+(11)/(6)

Combine all similar terms in the polynomial 9x-9-6x+4.
(3x-5)/(6)=1-x+(11)/(6)

To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 6. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
(3x-5)/(6)=-x+1*(6)/(6)+(11)/(6)

Complete the multiplication to produce a denominator of 6 in each expression.
(3x-5)/(6)=-x+(6)/(6)+(11)/(6)

Combine the numerators of all fractions that have common denominators.
(3x-5)/(6)=-x+(6+11)/(6)

Add 11 to 6 to get 17.
(3x-5)/(6)=-x+(17)/(6)

Multiply each term in the equation by 6.
(3x-5)/(6)*6=-x*6+(17)/(6)*6

Simplify the left-hand side of the equation by canceling the common factors.
3x-5=-x*6+(17)/(6)*6

Simplify the right-hand side of the equation by simplifying each term.
3x-5=-6x+17

Since -6x contains the variable to solve for, move it to the left-hand side of the equation by adding 6x to both sides.
3x-5+6x=17

Since 3x and 6x are like terms, add 6x to 3x to get 9x.
9x-5=17

Since -5 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 5 to both sides.
9x=5+17

Add 17 to 5 to get 22.
9x=22

Divide each term in the equation by 9.
(9x)/(9)=(22)/(9)

Simplify the left-hand side of the equation by canceling the common factors.
x=(22)/(9)

Answer 3

woah omg I love you thanks so much !!!!!!!!

Answer 4

your welcome

Answer 5

If I'm reading your original equation correctly, I got x = 1.

Answer 6

actually ya dmancine your right I just checked the answer, could you possibly tell me how you got it ?

Answer 7

First, I'm going to use the Equation editor to make your equation easier to read.\[\frac{3}{2}(x-1)-\frac{x+2}{3}=1-\frac{x-11}{6}\]Is that the actual problem, or did I misunderstand?

Answer 8

Ya you got it right, thats the actual problem

Answer 9

The first thing I would do is get rid of the denominators by multiplying both sides by the same number. What number should we use?

Answer 10

Alright , I used 6 which was the lowest common multiple.

Answer 11

also the last part is = 1 - x + 11 over 6

Answer 12

You should use parentheses to group things together so it's not ambiguous. Do you mean (1-x+11)/6 or 1-((x+11)/6)? Or did I just flip a sign when I wrote the equation before? (It looks like I just flipped the sign. Using x+11 yields x=1, which you said is right.)

Order of operations is important. Multiplication and division happen before addition and subtraction. If you type x+11/6 that means
\[x+\frac{11}{6}\]If you mean\[\frac{x+11}{6}\]you need to use parentheses to override the normal order of operations: (x+11)/6. Mathematics has a very precise language for expressing these things, and if we all use it we can communicate unambiguously.

Just so we're clear, is this the problem:
\[\frac{3}{2}(x-1) -\frac{x+2}{3}=1-\frac{x+11}{6}\]

If so, post what you got just after you multiplied by 6.

Answer 13

sorry it was (x+11)/6 and I have 9x-9-2x+2=1-x+6

Answer 14

I think you've done more than one step there. Just multiply by 6 and don't distribute into the parentheses.

Answer 15

ya i think i did so it would be 9(x-1)-2x+2=1-x +6

Answer 16

Let's go one term at a time. What do you get when you multiply each of these terms by 6:\[\frac{3}{2}(x-1)\]\[-\frac{x+2}{3}\]\[1\]\[-\frac{x+11}{6}\]Just do the multiplication. Don't distribute. (You got the first one right, by the way.)

Answer 17

alright awesome, i got

9(x-1)

- (6x+2)/3

6

- (6x + 66)/6

Answer 18

I think that second one is a little wrong still. Also, you're still distributing the 6 into the parentheses. Can you leave it out and leave the (x+2) and (x+11) parts the way they are?

Answer 19

(I guess I might be confusing you by saying "into the parentheses" when there aren't actually any parentheses there. There's kinda "implied" parentheses in the 2nd and 4th terms because when you write them like -(x+2)/3 the parentheses show up.)

Answer 20

ya i kinda got that part although its still a little confusing but would I just be multiplying the denominator by 6 thenand leaving the top part out ?

Answer 21

Yes. The term\[-\frac{x+2}{3}\]really means the same thing as \[-\frac{1}{3}(x+2)\]if that helps. Do you understand why?

Answer 22

uhm that helps but i dont understand

Answer 23

oh does the (-) sign equal 1 and you just multiply (x+2)

Answer 24

Well, taking the negative of something is the same as multiplying by -1. Also, dividing by 3 is the same as multiplying by 1/3. Do you understand both of those concepts?

Answer 25

Okay ya I get that.

Answer 26

Also, when x+2 is in the numerator you're dividing the whole quantity x+2 by the denominator.

Answer 27

Uhm can you show me like a step I dont get that Im more of a visual learner.

Answer 28

Does this help?\[-\frac{x+2}{3} = -\frac{(x+2)}{3}\]

Answer 29

uhm whats it become ?

Answer 30

oh nevermind I got that.

Answer 31

So, before we do anything else, can you write the term\[-\frac{x+11}{6}\]as a fraction times (x+11), like I did above for the other term?

Answer 32

like this ? -((x+11))/6

Answer 33

oops (x+11)/6

Answer 34

I was talking about when I did this:\[-\frac{x+2}{3} = -\frac{1}{3}(x+2)\]See the fraction out front?

Answer 35

oh would it be ? 1/6 (x+11)

Answer 36

Yes, except you lost the minus sign.

Answer 37

oh oops forgot about that

Answer 38

ok so its - 1/6 (x+11)

Answer 39

Right.

Answer 40

ok after these steps I keep distributing the 6 and I keep getting different answers

Answer 41

Ok. Go back to the post where I had the 4 terms listed by themselves, and show me what you get for each of them when you just multiply them by 6. Don't distribute.

Answer 42

ok I have

6(x-1)
-2(x+2)
6
-6(x+11)

Answer 43

The first one's wrong, but you did it right the first time (many posts ago). And the last one's wrong. Tell me how you got what you got for them.

Answer 44

oh the first ones 9(x-1) i just messed that up and the seconds -1(x+11)

Answer 45

Yes! Okay. Now we have
9(x-1)
-2(x+2)
6
-1(x+11)
For all but the third one, distribute the number into the parentheses.

Answer 46

awesome so
9x-1
-2x+(-4)
6
-1x +(-11)

Answer 47

First one's a little wrong.

Answer 48

oh 9x - 9 sorry Im really tired

Answer 49

lol. I understand. And you did the other ones right, so I figure you know what you're doing with distributing. But we have to get every little step right.

Okay. It'll be easier to deal with if you change the things like +(-4) into just a subtraction. And -1x is just -x. So, do those steps.

Answer 50

ya thats true its helping alot.

so it would be

9x - 1
-2x-4
6
-x-11

Answer 51

I'll assume the first was just a typo again.

Now, we need to assemble those pieces back into the equation we took them out of. Try doing that.

Answer 52

I'll assume the first was just a typo again.

Now, we need to assemble those pieces back into the equation we took them out of. Try doing that.

Answer 53

i think I got it

9x - 9 - 2x-4=6 - x-11

9x+x-2x=6-11+9+4

8x=8

x=8/8

x=1

Answer 54

Yep. But make sure you understand how we went from the original problem to the equation we got after multiplying by 6 and distributing.