Having Trouble With These Multi-Step Equations

[Denver]

How would I go about solving a problem

10h=8h+6

and a problem like this
as well...

8=4(3x+5)

 

[Deleted member 4993]

How would I go about solving a problem

10h=8h+6

and a problem like this
as well...

8=4(3x+5)

go to:

http://www.purplemath.com/modules/solvelin.htm

for a quick review.

If you are still stuck, post back showing your work and indicate exactly where you are stuck.

 

[o_O]

For questions like your first one, what you're trying to do is get the unknown variable (the letter h) on one side of the equal sign and all the numbers on the other side using all the rules you know. The main one is: what you do to one side, you do to the other.

I'll do an example question and see if you can solve the other.

6x + 7 = 9x - 5
6x - 6x + 7 = 9x -6x - 5
(We want all the x's on one side, so I chose the left side and subtracted the 6x to get rid of it. Since I did that, I MUST do the same to the other)

0 + 7 = 3x - 5
(When adding or subtracting terms with the same variables (or letters), for example 8a + 4a, we just add or subtract the coefficients (numbers in front of the letters) to get 12a)

7 = 3x - 5
(We want x all by itself so that -5 is in the way. So let's get rid of it by adding 5 to the right hand side. That means we have to do the same to the left in the next step)

7 + 5 = 3x - 5 + 5

12 = 3x
(Now, there is just the 3 in front of the letter to get rid of. How do we get rid of it if we're multiplying 3 by x? We do the opposite by dividing by 3 as shown in the next step)

\(\displaystyle \frac{12}{3} = \frac{3x}{3}\)

Then we get:
4 = x or if you like the x on the left side: x = 4.


For you're second problem, when dealing with brackets you multiply the term OUTSIDE the brackets with EACH term INSIDE the brackets. For example:
5(6x + 5x² + 3) = (5)(6)x + (5)(5)x² + (5)(3) = 30x + 25x² + 15

Then use what you understood from my first example and see where you go!

 

[Denver]

For questions like your first one, what you're trying to do is get the unknown variable (the letter h) on one side of the equal sign and all the numbers on the other side using all the rules you know. The main one is: what you do to one side, you do to the other.

I'll do an example question and see if you can solve the other.

6x + 7 = 9x - 5
6x - 6x + 7 = 9x -6x - 5
(We want all the x's on one side, so I chose the left side and subtracted the 6x to get rid of it. Since I did that, I MUST do the same to the other)

0 + 7 = 3x - 5
(When adding or subtracting terms with the same variables (or letters), for example 8a + 4a, we just add or subtract the coefficients (numbers in front of the letters) to get 12a)

7 = 3x - 5
(We want x all by itself so that -5 is in the way. So let's get rid of it by adding 5 to the right hand side. That means we have to do the same to the left in the next step)

7 + 5 = 3x - 5 + 5

12 = 3x
(Now, there is just the 3 in front of the letter to get rid of. How do we get rid of it if we're multiplying 3 by x? We do the opposite by dividing by 3 as shown in the next step)

\(\displaystyle \frac{12}{3} = \frac{3x}{3}\)

Then we get:
4 = x or if you like the x on the left side: x = 4.


For you're second problem, when dealing with brackets you multiply the term OUTSIDE the brackets with EACH term INSIDE the brackets. For example:
5(6x + 5x² + 3) = (5)(6)x + (5)(5)x² + (5)(3) = 30x + 25x² + 15

Then use what you understood from my first example and see where you go!

For the firstr;
10h=8h+6
-8h..-8h
----------
2h..0
2h/6=0.3

doesn't seem right im not sure exactaly

 

[o_O]

10h - 8h= 8h - 8h + 6
2h = 0 + 6 (You didn't do anything to the 6 so it stays here)

Remember, we are trying to get h all by itself on one side of the equal sign.

 

[Denver]

oh so it's 6 divided by 2? making it 3


because 10x3=30

 

[o_O]

Yep! Exactly. And you can always check your answer by plugging h = 3 back into your original equation to see if it actually works:

10h = 8h + 6
10(3) = 8(3) + 6
30 = 24 + 6
30 = 30

So h = 3 really does work.

 

[Denis]

How would I go about solving a problem
10h=8h+6

Denver, that's quite basic; are you a student or learning on your own?

 

[Denver]

Student, learned it all last year but forgot it over summer.

 

[Denis]

Student, learned it all last year but forgot it over summer.

Of course.