Help with algebra please?

Question

I was hoping to get some help with these equations. I haven't done algebra in school yet so I want to get a head start. If anyone could give me the answers and explain how they got them, I would greatly appreciate it :) thank you

/ = division

7(+ -1) /4 + 8 = 12

3w + 2 = 10 - w

10z + 21 = -3 - 2z

p + 4 = 2p - 3

3 + 4q = 25 - 7q

6r + 2(4r - 3) = 6 + 5(r/3)

Jenny is 6cm taller than Penny. If their total height is 322cm, how tall is Penny?

3 consecutive odd numbers add up to 18. what are the 3 numbers? ( let x be the 1st number)

Answer 1

I'm guessing the first one means + or -, pick plus, it makes the equation true

I'm going to show you one and you can do the others, this is basic Algebra 101

3w +2 = 10 - w

you can do the same thing to both sides an equation and it will still be true, like this

3w + 2 +w = 10 -w +w  (I added w to both sides, they are still equal)

4w +2 = 10  (just gathered like terms, see on right side w's cancelled)

4w +2 -2 = 10 -2 (I subtracted 2 from both sides)

4w = 8 (gathered like terms)

4w/4 = 8/4 (divided both sides by 4, still equal)

w=2 (completed the division and you have the answer

Just do the same for the rest of the equations, I'll show you the last one cuz its a little harder

6r +2(4r-3) = 6 +5(r/3)

3 * (6r + 2(4r-3) =  3 * (6+5(r/3)) (multiply both sides by 3)

18r +6(4r-3) = 18 +5r  (complete the mulltiplication)

18r +24r - 18 = 18 +5r (distribute the multiplying)

18r +24r -18 +18 = 18 + 5r +18 (add 18 to both sides)

42r=36+5r (gather like terms)

42r - 5r = 36 +5r -5r (subtract 5r from both sides)

37r = 36

r= 36/37

Now the word problem you can do it like this

322 - Penny = 6

-Penny = 6-322

Penny = -6+322

Penny = 316

Last one, since they are consecutive this makes it easy

x is the first #

x+1 is the 2nd (its one more(consecutive)

x+2 is the 3rd

Total = 18 = 1st number + second + third = x + x+1 + x + 2

18=3x+3

18 - 3 = 3x + 3 -3

15 = 3x

15/3 = 3x/3

5 = x

Answer 2

Hi,

Here it goes:

Legend:

eqn=equation; left side = Ls; right side = Rs; no. = number

7(+ -1) /4 + 8 = 12 (there's something wrong with this eqn, pls double check as it is not an algebraic eqn)

10z + 21 = -3 - 2z

10z+2z = -3 -21 (no. with z to the Ls of the eqn and no. without z to the Rs; note that the sign on the left of a number changes when it is brought to the opposite side of the eqn. Eg. -2z moves from Rs to Ls and changes to +2z. When there is no sign on the left, e.g. 10z, it means +10z)

12z = -24

z = -24/12

z = -2

p + 4 = 2p - 3

p-2p = -3 -4

-p = -7 (note that the negative sign cancels out since it is on both sides of the eqn)

p = 7.

3 + 4q = 25 - 7q

4q+7q = 25 - 3

11q = 22

q = 2

6r + 2(4r - 3) = 6 + 5(r/3)

6r + 8r-6 = 6 +5r/3 [Open up the bracket and multiply the no. outside into each no. in the bracket]

6r+8r-5r/3 = 6+6

14r-5r/3 = 12

42r-5r = 12x3 [when the no. is the denominator in the Ls and goes over to the Rs, the sign changes from division to multiplication and so it becomes the numerator]

37r = 36

r = 36/37

Jenny is 6cm taller than Penny. If their total height is 322cm, how tall is Penny?

Let Penny's height be x cm. Jenny's height would then be (x + 6)cm.

x+ (x+6) = 322

2x +6 = 322

2x = 322-6

2x = 316

x = 316/2

x = 158

Hence, Penny is 158 cm and Jenny is 164 cm.

3 consecutive odd numbers add up to 18. what are the 3 numbers? ( let x be the 1st number) [There's something wrong with this qn as the sum of 3 odd no.s should add up to an odd no. not an even no.] Hence, if the qn were 3 consecutive even nos, the following would apply:

Since the 1st no. is x, 2nd no. is x+2, 3rd no. is x+4 (cos, when you add 2 to an even no., you get the next even no.e.g. 2, 4, 6)

x+x+2+x+4 = 18

3x +6 =18

3x = 18-6

3x = 12

x=12/3

x=4

Therefore, the 3 nos. are 4,6,8.

Hope it helps and do explore algebra further on your own. It's fun :)

Answer 3

I won't give you the answers, by I will explain what you need to do.

In an equation, you have two values that are THE SAME. So, for example, if I were to subtract 2 from both those values they will still be equal to each-other.

3w + 2 = 10 - w

3w + 2 IS 10 - w

We could also say that:

3w = 10 - w -2  (Because I subtracted 2 from both sides)

3w + w = 10 - 2  (Because I added w to both sides)

4w = 8  (3w+w is 4w; 10-2 is 8)

w = 2 (I divided both sides by 4)

Answer 4

3w+2 = 10 - w

4w + 2 = 10

4w = 8 divide 8 by 4

w= 2

the others work on basically the same principles