Simplifying and Solving Equations?

Question

Hi, I need help trying to figure out how to do some math problems. I'm totally confused.

3b - 5 - 2b = 5
b=

3(x - 4) = 15
x =

5n + 4 - 8n = - 5
n=

36 = 4 (q - 5 )
q =

Here are a few of the examples I have to do. Any step by step help would be appreciated. I have about 30 problems to do. Thanks. so much

Answer 1

b - 5 = 5 (combine the like terms 3b - 2b = b)
b = 10 (add 10 to both sides)

3x - 12 = 15 (distribute the x in the parenthesis)
3x = 27 (add 12 to both sides)
x = 9 (divide both sides by 9)

That should get you started

Answer 2

This is gonna be hard to show but I'll try:D
I'm not the best at explaining, but here goes...
So lets do the first question:

I'm taking it this question is giving an equation, and then asking for a value for b. I've numbered the key steps.
If so then:

3b - 5 - 2b = 5
(we can rearrange this to look more simpler)
(1.) 3b - 2b - 5 = 5
(here we can see that we can simplify the question by dealing with the two common factors, that is, the 3b and 2b)
Subtracting 2b from 3b gives:
(2.) 1b - 5 = 5
Now it kinda gets a bit confusing.
Because there is a negative 5 on the left side (of the equals sign), we can remove it by adding 5.
1b - 5 (+5) = 5
But to do this, we need to also add 5 to the right hand side (of the equals sign), so that the equation is kept balanced
(3.) 1b - 5 (+5) = 5 (+5)
Solving,
1b - 0 = 10
(4.) Thus, b = 10

Hope you can follow? Or that this helps slightly?

For the second question, expand out the brackets. The (x - 4) is bracketed to show that both the x and - 4 are mutiplied by 3. That is, if you expand you will get 3x - 12 = 15. Rearranging and taking similar steps to the first question, we get 3x - 12 (+12) = 15 (+12) ( adding 12 to get rid of the -12) Therefore, 3x = 27 (now to get rid of the 3 on the lefthand side, we must divide by 3 on both sides of the equation) ( 3x / 3 = 27 / 3 ) therefore x = 9

For the third, takes similar steps to both the first and second. Rearrange to give 5n - 8n +4 = -5 Dealing with the common factors, that is, the 5n and - 8n we get -3n +4 = -5 Now we need to get rid of the +4, so subtract 4 from both sides giving -3n +4 (- 4) = -5 (- 4) Which gives -3n = -9 Now using the same method as in the second question, we must divide both sides by -3, to remove the -3 on the LHS (lefthandside)
giving -3n / -3 = -9 / -3 Therefore, n = 3 (dividing a negative by a negative gives a positive)

Lastly, the fourth question, expand the brackets like in question two, giving, 36 = 4q - 20 Add 20 to both sides to remove the - 20 36 (+ 20) = 4q - 20 (+20) giving 56 = 4q
Divide both sides by 4 to remove the 4 on the RHS giving
56 / 4 = 4q / 4 Therefore 14 = q

Hope my answer has helped in some sortv way and not just confused you further! Gd luck with it

Answer 3

3b - 5 - 2b = 5 : original
b - 5 = 5 : combine the b's
b = 10 : add 5 to both sides

3(x - 4) = 15 : original
3x - 12 = 15 : distribute the 3 over the parentheses
3x = 27 : add 12 to both sides
x = 9 : divide both sides by 3

5n + 4 - 8n = -5 : original
-3n + 4 = -5 : combine the n's
-3n = -9 : subtract 4 from both sides
n = 3 : divide both sides by -3

36 = 4(q - 5) : original
36 = 4q - 20 : distribute the 4 over the parentheses
56 = 4q : add 20 to both sides
14 = q : divide both sides by 4
q = 14 : you can always flip an equation's sides. Some people do this first -- and your 2nd line would have been 4(q - 5) = 36.

Answer 4

try to group similar variables on each side of the equation. on the first one, make it appear this way:

3b - 2b = 5 + 5 (since it came from the left, it changed sign from negative to positive, thus the plus sign)
now you have a simplified equation of :
b = 10 ---> check to see that the value is correct by substituting 10 to the variable b on the original equation, which will give you

3(10) - 5 - 2(10) = 5
30 - 5 - 20 = 5
5 = 5

on the second example, simplify it first by multiplying:
3 (x - 4) = 15
3x - 12 = 15
3x = 15 + 12
3x = 27 ---> divide 3 on both sides so you only have x on the left
x = 27/3
x = 9 is the final answer

perform the same process on the next examples. remember that you have to simplify the equation first. follow the MDAS rule wherein you Multiply first, then Divide before Adding and/or Subtracting

Answer 5

group like terms 3b - 2b -5 = 5 => b - 5 = 5
+ 5 on both side b = 10

distribute the expression 3x - 12 = 15
add 12 on both side 3x = 27
divide both side by 3 x = 9

4 - 3n = -5
-3n = -9
n = 3

36 = 4q - 20
56 = 4q
q = 14

Answer 6

OK here is how to do the first two.
1) gather similar terms.
3b-5-2b=5
3b-2b-5=5
b-5=5
2) group similar terms by addition
3b-5+5=5+5
3) solve
b=10

For the second.
1) multiply or divide to remove the coefficient of x
3(x-4)=15
3(x-4)/3=15/3
x-4=5
2) collect terms by addition or subtraction
x-4+4=5+4
x=9

The remaining problems are just like the first two.

Answer 7

3b-2b=10 I just threw the 5 to the other side so i get the b's
b(3-2)=10 i factored out the b
therefore b=10/1 or just 10

3x-12=15 i just multiplied it thre
from here its just like the first one
3x=27
x=9

5n-8n=-9
n(5-8)=-9
n=-9/(5-8) n= -9/-3 n= 3

these are all similar. just get it so that the variable is by its self and factor it and just use your rules of algebra to solve for the variable

Answer 8

okay ready?
on the first one, combine like terms. So you would subtract 2b from 3b
so you get
-b - 5 = 5
ok now add five to both sides.
-b = 10
so therefore
b = -10

now the next one.

distribute the three to the x and the -4

3x - 12 = 15
add 12 to both sides.

3x = 27
divide each side by three and you get

x=9

next one, do the same as the first one with the new numbers.

and the last one do the same as the second.

Answer 9

To amplify ability to "blow up" the parentheses via observe the outdoors to the interior. See, 3(a + 2) rather ability 3 * a + 3 * 2, or 3a + 6 4a + 3(a + 2) 4a + 3 * a + 3 * 2 4a + 3a + 6 7a + 6 3(2x - a million) = 21 3 * 2x - 3 * a million = 21 6x - 3 = 21 6x = 24 x = 4 i do no longer think of you published 2 properly, with the aid of fact this is not of the comparable form. a million + 7u = 25 7u = 24 u = 24/7

Answer 10

3b - 5 - 2b = 5
3b-2b-5=5
b-5=5
b=10


3(x - 4) = 15
3x-12=15
3x=27
x=9


5n + 4 - 8n = - 5
5n-8n+4=-5
-3n=-9
n=3


36 = 4 (q - 5 )
36=4q-20
56=4q
14=q