Trying again to help my 8th grade daughter with algebra...simplify each expression: -w+4(w+3) I don't just ?

Question

want answers...I want to know how you got it...5(b+4)-6b...-4x+3(2x-5)

2(3a+2)...-4+2(3+d)

I think if I had a little explanation I could figure out the rest...but it's been a long time since I did 8th grade algebra.

HELP!!

Answer 1

1.  5(b+4) is equivalent to  (5)(b) + (5)(4).  You multiply each item in the parenthesis by the 5.   That leaves you with 5b+20.  Then it is simple algebra from here.  

Subtract 20 from each side to isolate 5b

5b +20 -20 = 0 -20 =      

5b = -20

Now divide each side by 5

5b             -20

___    =   _____

5                  5

b = -4

The rest follow the same concept as problem 1

2.  -4x + 3(2x-5)

-4x + (3)(2x) - (3)(5) =

-4x +6x - 15

Now combine the like terms (x)

2x -15 =

2x = 15

x = 15 / 2

3.  2(3a+2) =

     6a+4

     6a = -4

     a = -4 / 6

4.  -4 + 2(3+d)

     -4 + 6+2d

    2 + 2d

    2d = -2

    d = -2 / 2

    d = -1

Answer 2

I'll give it a try:

a. -w+4(w+3)...distribute

-w^2-3w+4w+12... add the numbers and coefficient of the same kind

= -w^2+w+12... ur answer

b. 5(b+4)-6b... distribute

5b+20-6b... add the same kind

= -b+20... ur answer

c. -4x+3(2x-5)

-8x^2+20x+6x-15

= -8x^2+26x-15

...the only thing that I am not sure is if you have to find the value of the coefficient, then that'll be different...

eg.

d. 2(3a+2)... if you just distribute, then

6a+4... will be the final answer but it can go as far as this

6a=-4... put "4" on the other side of the equal... before it was

6a+4=0... but now it's

6a=(-4)... then cancellation meaning in able to just retain the "a" you have to divide "6" on both side

6a/6=(-4)/6... so

a= -4/6 or a= -2/3

I amtrying to help... i hope i didn't add to your confusion...

=)

Answer 3

The key parts to these problems is knowing distribution rules.

a(b+c) is equal to ab + ac

For your first problem.....

5(b+4) - 6b

1) You must first distribute (multiply) the five into the b + 4

5(b+4) - 6b = 5b +20 -6b

2) You now combine like terms

5b - 6b + 20 = -1b +20

-1b + 20 is your final answer.

For Problem Number Two same story.....

-4x + 3(2x-5)

1) Distribute the three into both terms (2x-5)

-4x + 3(2x-5) equals becomes -4x + 6x - 15

2) Combine Like Terms

-4x + 6x - 15 becomes 2x -15

2x-15 is the final answer

Answer 4

every time there is a number next to a parenthesis like a(b+c), you have to distribute the number to all terms within the parenthesis

so in that case, you would do

a*b + a*c, which gives you ab+ac

Here are the solutions to your problems:

-w+4(w+3)

-w+4*w+4*3

-w+4w+12

3w+12

same concept with the others

5(b+4)-6b

5*b+5*4-6b

5b+20-6b

-b+20

-4x+3(2x-5)

-4x+3*2x+3*-5 (DON'T forget the negative on the -5)

-4x+6x-15

2x-15

2(3a+2)

2*3a+2*2

6a+4 (this one was pretty simple)

-4+2(3+d)

-4+2*3+2*d

-4+6+2d

2+2d

Good luck!

Tell your daughter to take her time and follow the order of operations!

Answer 5

-w+4(w+3)=0

(-w(w)+3w)+(4w+12)=0

-w^2+7w+12=0 ; just multiply each variable with the other variable then

                           combine like terms

5(b+4)-6b=0

5b+(4*5)-6b=0

5b+20-6b=0

-b+20=0

b=20

-4x+3(2x-5)=0

-4x+6x-15=0

2x-15=0

2x=15

x=15/2

2(3a+2)=0

6a+4=0

6a=-4

a=-2/3

-4+2(3+d)=0

-4+6+2d=0

2+2d=0

2d=-2

d=-1

Answer 6

Here is an important thing: consider each number/letter a different expression, and the sign goes with the number/letter to the right of it (for example, -w and +4). Also whenever you multiply a number by a letter you just put the number and the letter together. Example: 3 times x =3x. And after you do the hard part, you have to simplify the equation at the end by adding together number/letter combinations that have the same endings only. Example: -13x+6x=-7x.

1) u multiply each "expression" by each expression in the parentheses. So u multiply -w by w, -w*3, 4*w, and 4*3 to get -w squared -3w plus 4w + 12, and that simplifies to:

-w squared +w + 12 (because -3w + 4w=1w or just w)

2) in this case for know ignore the -6b and concentrate on the rule i stated above, so multiply 5*b to get 5b and 5*4 to get 20 to get 5b+20. then tack on the -6b at the end, and sense both 5b and -6b have common endings (b), you can put them together by adding to get:

-b+20

3) Use the rule. do -4x by 2x to get -8x squared (because a number/letter times itself is considered the number squared), -4x by -5 to get +20x (because a negative times a negative is always a positive), 3*2x to get +6x, and 3 by -5 to get -15. Simplify to get:

-8x squared +26x -15

4) The rule again, 2*3a is 6a, and 2*2 is 4 so the answer is:

6a+4

5) More rule (kind of repetitive but that's algebra). -4*3 to get -12, -4 by d to get -4d, 2*3 to get 6, and 2 by d to get 2d, and that simplifies to:

-6-2d

I hope that helped!!

(By the way I am only 14 and I'm gonna b a freshman in high school)

Answer 7

-w + 4 (w + 3)

-w + 4w + 12

3w + 12

5 (b + 4) - 6b

5b + 20 - 6b

-b + 20

-4x + 3 (2x - 5)

-4x + 6x - 15

2x - 15

ask if you need more help in figuring it out : )

Answer 8

i believe you just distribute. the 1st would turn into 5b+20-6b then you would simplify that even more to -b+20.

the 3rd would be 6a+4. you just multiply the number on the outside by the numbers on the inside.

i hope i helped haha :]

Answer 9

-w+4(w+3).  Distribute the 4 across the parens.

-w+4w+12.  Add up the like variables (-1w and +4w).

3w+12.  Done.

Answer 10

1. -w + 4(w + 3)

first, use the distributive property and multiply each of the terms in parentheses by 4.

-w + 4w + 12

now combine like terms.

3w + 12

if you wanted to get really technical, you could now factor out the greatest common factor (3 in this case).

3(w + 4)

2.  5(b + 4) - 6b

once again, distribute the five to each of the enclosed terms.

5b + 20 - 6b

and combine like terms again.

20 - b

3. -4x + 3(2x -5)

where to go from here?  you guessed it, distributive property!  : )

combine like terms to finish off.

-4x + 6x -15  -->  2x - 15

4.  2(3a + 2)

i think you know what to do...

6a + 4

5.  -4 + 2(3 + d)

now distribute, combine like terms, and undistribute (gcf).

-4 + 6 + 2d  -->  2d + 2  -->  2(d + 1)

hope this completely refreshed your memory!  : )

Answer 11

ok...

1st multiply  -w*w = -w squared

2nd multiply  -w*3 = -3w

3rd multiply  4*w = 4w

4th mutiply  4*3 = 12

answer -w2-3w+4w+12

simplified -w2 + w +12

(the -w2 is negative w squared)

hope this helps!

Answer 12

this is a method i learned last year

  multiply                                  -w+4(w+3)

First terms                               -w+-3w+4w+12

Outter terms                    

Inner terms

Last terms

FOIL

then add the like terms         -w+1w+12