Please help with Math?

Question

I need to check my daughters Homework!

13. 12p+6-3p

14. 9+3k=2k-12

15. fraction 5/6t+4=2-1/6t

18. 3(z-2)+6=5(z+4)

20. 28-14z=negative24+12z

23. fraction u/0.3=4u+6.28

25. 0.3x-15=0.2x-5

Answer 1

I'm assuming for all these problems we need to solve for the variable. I'll solve each one for you and show you how, in case you have to show your daughter.

13. 12p + 6 - 3p

Here we're not going to be able to solve, because there's no equal sign. The only thing we can do is simplify by combining like terms. We have a 12p and a -3p. We can combine that. We end up with 9p. We can't combine +6 with anything so we are finished. Our answer is:

9p + 6

14. 9 + 3k = 2k - 12

Here we still want to combine like terms. However since we have an equal sign, we have to be careful. Anything we do to one side of the equation we have to do to the other side (in order to keep the equation equal).

We have 3k on the left and 2k on the right. These are positive. Since we want to move the 2k to the left we'll have to subtract 2k from both sides. This will put our k's together.

9 + 3k (-2k) = 2k (-2k) - 12 Notice how 2k and -2k cancel each other on the right.

We're left with:

9 + 1k (or just k) = -12

Now to get k by itself we have to subtract 9 from both sides. Again because 9 is positive and you undo that by subtracting.

So...

9 (-9) + k = -12 (-9) Again notice how 9 and -9 cancel on the left

We're left with:

k = -21 (-12 - 9 = -21)

That's our answer, because we have our variable equal to some value.

15. 5/6t + 4 = 2 - 1/6t

Here the idea is exactly the same as above, only we're working with fractions.

Let's start by adding 1/6t to both sides. This will combine our t's. Notice how we're adding this time because -1/6t is negative and to undo that we must add.

5/6t (+1/6t) + 4 = 2 - 1/6t (+1/6t) Notice the -1/6t and + 1/6t cancel on the right.

We're left with:

6/6t + 4 = 2

6/6t is the same as 1t (because 6 over or divided by 6 equals 1) So...

t + 4 = 2

To get t by itself we'd have to subtract 4 from both sides. Again since 4 is positive we undo this by subtracting.

t + 4 (-4) = 2 (-4) Notice how the +4 and -4 cancels.

We're left with:

t = -2

That's our answer.

18. 3(z - 2) + 6 = 5(z + 4)

This problem tests our knowledge of the Order of Operations. We always take care of parenthesis and what's attached to them first. So before we do anything let's distribute through to get rid of our parenthesis.

Working with the left side of the equation...

3(z - 2)

Multiply 3 * z and 3 * -2 we get 3z -6 (3z + -6 is the same as 3z - 6)

The left looks like this:

3z - 6 + 6

Working with the right side of the equation...

5(z + 4)

Multiply 5 * z and 5 * 4 we get 5z + 20

The right looks like this:

5z + 20

So our new entire equation looks like:

3z - 6 + 6 = 5z + 20

If we combine like terms we can see that -6 and +6 cancel. So let's rewrite like this:

3z = 5z + 20

Now if we subtract 3z from both sides to combine our z's we'll get...

3z (- 3z) = 5z (- 3z) + 20

0 = 2z + 20 Notice 3z - 3z = 0, so don't lose your equal sign.

Let's subtract 20 from both sides.

0 (- 20) = 2z + 20 (- 20)

-20 = 2z

Finally to get z by itself let's divide both sides by 2. Because z is being multiplied by 2 we have to undo that by dividing.

-20(/2) = 2z(/2) Notice 2/2 = 1 so on the right we're left with 1z or z

-10 = z

That's your answer.

20. 28 - 14z = -24 + 12z

This ones a bit simpler again. Notice how I'm moving the variables together so that it ends up positive. You don't want to have a negative variable. So I'm not going to subtract both sides by 12z I'm going to add 14z to both sides.

28 - 14z (+ 14z) = -24 + 12z ( +14z)

Simplify

28 = -24 + 26z

Let's add 24 to both sides

28 ( + 24) = -24 (+ 24) + 26z

52 = 26z

Finally we'll divide both sides by 26 to get z by itself

52(/26) = 26z(/26)

Our answer...

2 = z

23. u/0.3 = 4u + 6.28

This one looks a bit scarier but it's not really. A couple problems ago we undid multiplication by division. In this one, we need to undo division by multiplication.

So let's multiply both sides by the denominator (number on the bottom)

u/0.3 (* 0.3) = (4u + 6.28) (*0.3) Notice here that we're multiplying each side by 0.3 not just "4u"

(Again 0.3u/0.3 is 1u or just u *When you multiply fractions simply multiply across so u/0.3 * 0.3/1 = 0.3u/0.3 **0.3/1 is the same as 0.3 because anything divided by 1 is itself)

u = (Distribute by multiplying 4u * 0.3 and 6.28 * 0.3) 1.2u + 1.884

Looks ugly but let's stay with it.

u = 1.2u + 1.884

Again I like to keep my variables positive so I'll subtract u from both sides.

u (- u) = 1.2u (- u) + 1.884

0 = 0.2u + 1.884

Let's subtract 1.884 from both sides.

0 (- 1.884) = 0.2u + 1.884 (- 1.884)

-1.884 = 0.2u

Finally divide both sides by 0.2

-1.884(/0.2) = 0.2u(/0.2)

-9.42 = u

That's your answer. Finally last one.

25. 0.3x - 15 = 0.2x - 5

Same idea as the above problems. Let's subtract 0.2x from both sides

0.3x (- 0.2x) - 15 = 0.2x (- 0.2x) - 5

0.1x - 15 = -5

Let's add 15 to both sides

0.1x - 15 (+ 15) = -5 (+ 15)

0.1x = 10

Finally let's divide both sides by 0.1 to get x by itself.

0.1x(/0.1) = 10(/0.1)

x = 100

Hope that helped. The key to remember here is, undo addition with subtraction, subtraction with addition...and undo multiplication with division, division with multiplication. Remember your signs. You'll be fine.

In Summary your answers:

13. 9p + 6
14. k = -21
15. t = -2
18. -10 = z
20. 2 = z
23. -9.42 = u
25. x = 100

Good Luck with your daughter's math.

Answer 2

12p+6-3p=9p+6

9+3k=2k-12
k = -21

5/6t+4=2-1/6t
t = -2

3( z-2) +6 = 5( z+4)
3z-6 + 6 = 5z + 20
- 2z = 20
( - 1 )-z = 10
z = -10

28 - 14z = - 24 + 12z
- 26z = - 52
- z = -2
( -1 ) -z = -2
z = 2

u/0.3 = 4u + 6.28
is this a mistake ?

0.3x - 15 = 0.2x - 5
0.1x = 10
x = 100

Answer 3

13. This question cannot besolved with the given information. I have run inyo problems like this before in math competitions. (it is probably a typo). However the book, workshhet etc. that the problems derive from may give a value for p. In this case siply substitute whatever that number is for p. (example: p=2; 12p+6-3p; 12*2+6-3*2; 24+6-6; leading you to 24 as your answer. Moreover this may be a problem that equalls zero.in that case follow these steps to solve the problem 12p+6-3p=0; 9p+6=o; 9p=6; answer: p= 0.6 repeating or 2/3.

14. k = -3

15. t = -4

18. z = -10

20. z = 2

23. u = -9.375

25. x = 100

You may want to double check these as I did them in my head.

Answer 4

13 9p+6

k = -21

(5/6)t + 4 = 2 -(1/6)t (multiply both sides by 6

5t + 24 = 12 - 1t
6t = -12
t = -2


Last question, 25:
x = 100

Answer 5

I am maths trainer sending you this guidelines: one million) Do no longer repair distinctive time, two) Interest is the motivating aspect to study arithmetic. three) very principal factor to be famous is "Practice Examples and Exercises best. four) Do no longer disregard any bankruptcy. five) if you're a pupil of state board,don't study something from out part the Text Book. 6) Refer prior 12 months questions. 6) if ISC, you will have to refer further books. 7) Interest and rough paintings with constructive could convey you one hundred percentsuccesses

Answer 6

13. 9p+6
14. k= -21
15. t= -2
18. z= -10
20. z= 2
23. u= -9.42
25. x=100

Answer 7

13. 9p +6

14. k = -21

15. t = -2

18. z = -10

20. z = 2

23. u = -9.42?

25. x = 100

Answer 8

13. 9p+6