Equations help?

Question

y - 8 + 2y = 10

2g + 3g + 5 = 0

4y + 9 - 7y = - 6

17 = 3(g + 3) - g

I tried a few on my own after being shown how to do some, but I don't get it.

Answer 1

1. y-8+2y=10
y-2y=18
-y=18
y=-18

2. 2g+3g+5=0
5g+5=0
5g=-5
g=-1

3. 4y+9-7y=-6
4y-7y=-15
-3y=-15
y=5

4. 17=3(g+3)-g
17=3g+9-g
8=3g-g
8=2g
4=g

Answer 2

Here's what you do. Start out by trying to get the variables on one side and the constants on the other.

Remember that everything you do to one side, has to be done to the other side. That's what keeps it equal.

y - 8 + 2y = 10
y - 8 + 8 + 2y = 10 + 8

To get the 8 on the other side of the equation, I add it to both sides. If it was originally y + 8, I would subtract it on both sides. The idea is to make it zero on one side.

y + 2y = 18

Now I'll add the variables together.

3y = 18

To isolate the y, I'll divide both sides by 3.

3y / 3 = 18 / 3

y = 6

Prove it by substituting 6 for y.

6 - 8 + 2(6) = 10
6 - 8 + 12 = 10
10 = 10

The last one is a little different.

17 = 3(g+3) - g
17 = 3g + 9 - g
17 = 2g + 9
17 - 9 = 2g + 9 - 9
8 = 2g
8/2 = 2g/2
4 = g

17 = 3 (4 + 3) - 4
17 = 17

You can do the rest now.

Answer 3

Hi! There are only a few things to remember about these types of questions:
1) Isolate the variable in the equation (y,g)
2) BEDMAS
3) Whatever you do to one side you do to the other (in your attempt to isolate the variable).
4) like terms!
I will try to do these step by step so you can understand

Here's how you should try to go about it:
1) Combine the like terms
2) Isolate the variables.

Do these while remembering the 2 and 3 up there!
1)
y - 8 + 2y = 10
With this equation you can see that y and +2y are like terms. And luckily they are on the same side. Add them together:
3y-8=10

Now you can see that you can see that you need to isolate the variable. How can we do that? First lets get rid of the negative integeer (-8) on the Left hand side. How can we get rid of it? We do the opposite! That means we add +8 to the left hand side, while bearing in mind that whatever we do to one side we do to the other:
3y - 8 +8 = 10 +8
3y = 18

Now we can see that all we have left to do is get rid of the 3y. Remember how we do the opposite? Well the opposite of multiply in dividing right. Remember whatever we do to one side we do to the other:
so:
(3y) / 3 = 18 / 3
y=6

And that's it :D

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Now I won't explain the next two in as much depth as it is the exact same concept. But I will show you the steps:
2g + 3g + 5 = 0
5g+5=0
5g+5-5=0-5
5g=-5
5g/5=-5/5
g=-1

4y + 9 - 7y = - 6

4y - 7y + 9 =-6
-3y + 9 = -6
-3y +9 - 9 = -6 - 9
-3y = -15
-3y/-3=-15/-3
y=5
---------------------------------------------------------------
17 = 3(g + 3) - g
This one is a tad more tricking as we have brackets involved. Brackets mean multiply. According to BEDMAS we should multiply before we add or subtract, thus:
17 = 3g+9 - g
17 = 4g+9
17-9 = 4g+9-9
8=4g
8/4=4g/4
2=g;

This is an important concept in math in which you should try to understand :). These skills will provide the foundation of knowledge in which you will need for years more of math. Just remember how to combine like terms, BEDMAS, and the rule: "whatever you do to one side you do to the other". Also remember the key is isolating the variable.

Also incase you have forgotten you should review your work with negative integers. For example, -x/(-1)=x. That is, a negative number divided by a negative number is a positive number. Or a negative times a negative is positive. These are crucial concepts for understanding such problems.

I hope this helps :)

Answer 4

y - 8 + 2y = 10
group the variables:
(add y + 2y)
3y - 8 = 10
segregate, variables on one side, non-variables on the other:
(add 8 to both sides)
3y = 18
get the variable by itself:
(divide both sides by 3)
y = 6

2g + 3g + 5 = 0
group the variables:
(add 2g + 3g)
5g + 5 = 0
segregate, variables on one side, non-variables on the other:
(subtract 5 from both sides)
5g = -5
get the variable by itself:
(divide both sides by 5)
g = -1

4y + 9 - 7y = - 6
group the variables:
(4y - 7y)
-3y + 9 = -6
segregate, variables on one side, non-variables on the other:
(subtract 9 from both sides)
-3y = -15
get the variable by itself:
(divide both sides by -3)
y = 5

17 = 3(g + 3) - g
distribute the multiplier:
(3 * g + 3 * 3)
17 = 3g + 9 - g
group the variables:
(3g - g)
17 = 2g + 9
segregate, variables on one side, non-variables on the other:
(subtract 9 from both sides)
8 = 2g
get the variable by itself:
(divide both sides by 2)
4 = g or g = 4 (I know my math teachers always liked the variable on the left. Don't know if yours would be that picky) ; -)

Hope that helps!!

Answer 5

QUESTION: Y-8+2Y=10

ANSEWER: Y = IDK