Help with algebra!!?

Question

Can someone help me answer these and explain how you got the answers please.......
x-5/8=7/8
2/3+3k/4+71/12
a/2+1/5=17
9y/14+3/7=9/14

Answer 1

first one
x-5/8=7/8

add 5/8 to both sides
get
x=12/8

Answer 2

x-5/8=7/8
x=7/8 + 5/8 [You can move terms from one side of the equation to the other as long as you change the sign
x=12/8 = 3/2 [Same denominator so just add numerators]

2/3+3k/4+71/12
I'm going to assume the second + sign is really an = sign
2/3 +3k/4 = 71/12
3k/4 =71/12-2/3 = 71/12 -8/12 = 63/12
3k = 4(63/12) = 63/3 =21
k = 7

a/2+1/5=17
a/2 = 17-1/5 = 16 4/5
a = 2(16 4/5) = 32 8/5 = 33 3/5

9y/14+3/7=9/14
9y/14 = 9/14 -3/7 = 9/14 - 6/14 = 3/14
9y = 14(3/14) = 3
y= 3/9 = 1/3

Answer 3

These problems can all be solved by remembering how to handle common denominators.

You can't add or subtract fractions unless they have the same denominators so you have to convert them.

The first problem already has common denominators. Both fractions are 1/8's so it can be handled directly by adding 5/8 to each side yielding x=12/8=3/2.

The next problem has denominators of 3, 4, and 12. The common denominator there is clearly 12. 3, 4, and 12 all divide into 12 evenly.

So, we have to make each fraction have a denominator of 12, without changing the value of that fraction.

We start with 2/3. We need to multiply the denominator by 4 to make it the common 12 we are looking for. If we also multiply the numerator by 4, the value of the fraction doesn't change. 8/12 is the same number as 2/3, but written in a way that it has a 12 for the denominator. The next fraction 3k/4, when multiplied top and bottom by 3, becomes 9k/12. The last fraction stays as 71/12. (or is that the mixed fraction 7 1/12?). Either way, the denominator is already 12.

8/12+9k/12+71/12
79/12+9k/12
(79+9k)/12

I suspect that problem had a typo because it wasn't an equation with an equal sign, but just an expression. Still, you can see how the process works.

The next one has denominators of 2 and 5. A good common denominator would be 10.

5a/10+2/10=17

now multiply both sides by 10

5a + 2 = 170
5a=168
a=168/5

See how if goes. I might suggest a common denominator of 14 for the last one. Go for it.

Answer 4

1)
x - 5/8 = 7/8
x = 7/8 + 5/8
x = 12/8
x = 3/2
x = 1 1/2

2)
Not sure if 71/12 or 7 1/12 but it would be simpifying the equation rather than having an answer

3)
a/2 + 1/5 = 17
5a/10 + 2/10 = 170/10
5a/10 = 170/10 - 2/10
5a/10 = 168/10
5a = 168
a = 168/5
a = 33 3/5

4)
9y/14 + 3/7 = 9/14
9y/14 + 6/14 = 9/14
(9y + 6)/14 = 9/14
9y + 6 = 9
9y = 3
y = 3/9
y = 1/3

have fun!

Answer 5

7/8 + 5/8 = 12/8 or 1 and 4/8

second one there is no = sign could be 71/12 - 8/12 +63/12
or 21/4 21/3 =7 k=7

(33.9)/2 +1/5 +17 33.9/2 +.2 = 17

y = .33 or 1/3 in the last example

Answer 6

x=1 3/8

Answer 7

When you do algebra problems like these, the goal is to get the letter(variable) on one side of the equation by itself. AND what you do to one side, you ALWAYS must do to the other.
a) x=7/8+5/8
I want x by itself, so I will add 5/8 to both sides because I know that -5/8+5/8=0. This will get x alone.

b)Is not an equation, but it is an expression. You forgot to put the equal sign in.

c) a/2=17-1/5
a=(17-1/5)*2
I want a on one side by itself. I have to get rid of 1/5 first by subtracting it from both sides of the equation. Then, I must multiply both sides by 2 because 2*a/2=a.

d) 9/14y=9/14-3/7
y=(9/14-3/7)*14/9

Remember, you want the variable alone.
What you do to one side you must do to the other.

Answer 8

1)x-5/8=7/8
Add 5/8 to both sides:
x=12/8

Check:
12/8-5/8=7/8
7/8=7/8

2)2/3+3k/4=71/12
Multiply 12 from both sides:
12(2/3+3k/4)=12(71/12)
8+9k=71

Subtract eight from both sides:
9k=63

Divide 9 from both sides:
k=7

Check:
2/3+3(7)/4=71/12
2/3+21/4=71/12
8/12+63/12=71/12
71/12=71/12

3)a/2+1/5=17
Multiply both sides by 10 to get rid of the fractions:
10(a/2+1/5)=10(17)
5a+2=170

Subtract 2 from both sides:
5a=168

Divide 5 from both sides:
a=168/5=33.6

Check:
(33.6/2)+(1/5)=17
16.8+0.2=17
17=17

4)9y/14+3/7=9/14
Multiply 14 from both sides:
14(9y/14+3/7)=14(9/14)
9y+6=9

Subtract 6 from both sides:
9y=3

Divide 9 from both sides:
y=3/9=1/3
y=1/3

Check
(9(1/3)/14)+3/7=9/14
3/14+3/7=9/14
3/14+6/14=9/14
9/14=9/14

Answer 9

x=12/8 add 5/8 to each side
k=7/16 subtract 2/3 from each side, multiply by 4 then divide by 3
a=33 3/5 subtract 1/5 from each side then multiply by two
y=1/3 subtract 3/7 from each side, multiply by 14 then divide by 9

Answer 10

you just isolate the variable, I'll give you an exemple and it's all the same for other tings:

5x - 7 = 3 here you do + 7 on each side witch make:
5x = 10 now you divise per 5 on each side
1x= 2 so it's mean that: x=2 here's your answer!

Answer 11

For increasing cubic binomials the final formula is as follows: (a + b) ^ 3 = a^3 + 3*a^2*b^a million + 3*a^a million*b^2 + b^3 on your case, a is x and b is -y^5 So (x - y^5)^3 = x^3 + 3*x^2*(-y^5)^a million + 3*x^a million*(-y^5)^2 + (-y^5)^3 Simplified: =x^3 - 3x^2*y^5 + 3x*y^10 - y^15 :D