I need help solving for the unknown in the equations?

Question

8y+6=3
3b+14=5b
4.5m-3=2m-0.5
7.3m-16=m+0.38
18n+2n=6n+11.2

Answer 1

Answer 1:
8y+6=3
8y = 3-6
8y = -3
y = -3/8

Answer 2:
3b+14=5b
3b = 5b -14
3b - 5b = -14
-2b = -14
2b = 14 (Minus signs cancel each other out)
b = 14/2
b = 7

Answer 3:
4.5m-3=2m-0.5
4.5m = 2m -0.5 + 3
4.5m - 2m = 2.5
2.5m = 2.5
m = 2.5/2.5
m = 1

Answer 4:
7.3m-16=m+0.38
7.3m = m + 0.38 + 16
7.3m - m = 16.38
6.3m = 16.38
m = 16.38/6.3
m = 2.6

Answer 5:
18n+2n=6n+11.2
20n = 6n + 11.2
20n-6n = 11.2
14n = 11.2
n = 11.2/14
n = 1.6/2
n = 0.8

Answer 2

This replaced into lovable sufficient of a difficulty for me to artwork this out intimately. because of the fact that many times f(x,y) = 0 would not have basically a single root {x,y}, this root must be an extrema, so we partial differentiate as follows: ?/?x(?(x² + a million) + ?((24 - x - y)² + 4) + ?(y² + sixteen) - 25) = x/(?(x² + a million)) - z/(?(z² + a million)) = 0 the place z = 24-x-y. fixing this gets x = z/2 and from that we get y = 24 - 3x. We do this lower back: ?/?y(?(x² + a million) + ?((24 - x - y)² + 4) + ?(y² + sixteen) - 25) = y/(?(y² + sixteen)) - z/(?(z² + a million)) = 0 the place z = 24-x-y as until now. fixing this gets y = 2z, and from that we get x = 24 - (3/2)y. From those 2 linear equations, we arise with: {x,y} = {24/7, ninety six/7}, confirming Rita's consequence. needless to say, this replaced into in accordance with guessing that it relatively is an extrema, i does no longer propose this as a known approach of looking roots. yet this is Dragan ok's poser, and so right here we are.

Answer 3

Okay, here is how I used to teach this to my tutoring students. You need to shift stuff around until all the numbers are on one side of the equal sign, and all the numbers with letters are on the other. Anytime you move a number or a number letter combination across an equal sign, the sign associated with the number changes. In other words, if the number started out as a negative, when you move it across the equal sign, it now becomes a positive, and visa versa.

Once you have shifted everything around, now you can combine like terms. So add up all the numbers with letters attached, and add up all the numbers too.

So looking at question 1. 8y+6=3 You want 8y by itself, so you are going to move the +6 across the equal sign. What happens to its sign?? It becomes negative. This gives you 8y = 3-6.

Add all the like terms (in this case add the 3 to the -6). 8y = -3
Now you need to get y by itself. To get rid of the 8, you need to divide it by 8 (8/8 = 1) Anything you do to one side of an equation, you must do to the other side. 8y/8 = -3/8. The 8's cancel out on the left therefore y = -3/8.

Let's look at Q.3. This is a bit more complicated, but not much. Get all the "m's" to the left of the equal sign an all the numbers to the right. Remember to watch your signs.

Good luck.

Answer 4

8y + 6 = 3
8y=3 - 6
8y = -3
y = -3/8

3b + 14 = 5b
14 = 5b - 3b
14 = 2b
b = 7

4.5m - 3 = 2m - 0.5
4.5m - 2m = - 0.5 + 3
2.5m = 2.5
m = 1

7.3m - 16 = m + 0.38
7.3m - m = 0.38 + 16
6.3m = 16.38
m= 2.6

18n + 2n= 6n +11.2
18n + 2n - 6n = 11.2
14n = 11.2
n = 0.8

Answer 5

8y+6=3 subtract 6 from both sides of =
8y=-3 now divide both sides by 8
y= -3/8 now you have isolated the variable "y"

3b+14=5b
14=2b
7=b

Answer 6

1. y= -3/8
2. b= 7
3. m=1
4. m= 2.6
5. n= 11.2/14

Answer 7

I'll do one for you and you can IM if you need more help if you want.

4.5m - 3 = 2m - 0.5

4.5m - 3 + 3 = 2m - 0.5 + 3

4.5m = 2m + 2.5

4.5m - 2m = 2m - 2m + 2.5

2.5m = 2.5

2.5m/2.5 = 2.5/2.5

m = 1

Answer 8

1.) y = -3/8

2.) b = 7

3.) m = 1

4.) m = 2.6

5.) n = 0.8

Sorry for any mistakes.

Answer 9

8y+6=3
8y=-3
y=-3/8

3b+14=5b
14=2b
b=7

4.5m-3=2m-0.5
2.5m=2.5
m=1

7.3m-16=m+0.38
6.3m=16.38
m=2.6

18n+2n=6n+11.2
14n=9.2
n=.6571

Answer 10

y=-5
thats all i know lol