I'm desperate for help =(?

Question

Okay, So I've spent, and trust me, a LONG time on this math quiz I'm doing. Yes, I'm homeschooled, but that doesn't make everything easy. These answers I cannot understand how to do. I've done everything else except for these 6.

1.) -2/3 + 3x = 1/3

2.) 15m - 4 = 12m - 3m - 16

3.) 8r + 4(2r - 6) = 4r - 4

4.) 3/5y + 2 = 8

5.) 4x - 3 + 2x - 2 - x = 10

6.) 0.18x - 11.65 = 0.41x - 9.58


If anyone can help, It's very much appreciated. I seriously have been doing MATH homework, quizzes since 10:30 this morning and I'm very tired and my eyes hurt but I have to catch up or else I fail. That's never good. But know this, I'm not gonna give up, I'm still gonna try. I'm just asking for some help. I've read through the readings for my homework but, no help there. anyone?

I don't know how to thank you guys. You guys are awesome. You guys helped me out alot. I saw what I was doing wrong so, thanks ^__^. Big help.

Answer 1

(1)

-2/3 + 3x = 1/3
+2/3 +2/3

3x = 1 .... x = 1/3

(2)

15m - 4 = 12m - 3m - 16
15m - 4 = 9m - 16
-9m -9m
6m - 4 = -16
6m = -16 +4
6m = -12
m = -2

(3)
8r + 4(2r-6) = 4r - 4
8r +8r - 24 = 4r - 4
16r - 24 = 4r -4
-4r -4r
12r -24 = -4
12r = -4 +24 = 20
12r = 20
r = 20/12 = 5/3

(4)
3/5y + 2 = 8
3/5y = 8 - 2 = 6
3/5y = 6
5(3/5y) = 5(6)
3y = 30
y = 30/3 = 10

(5)
4x - 3 + 2x - 2 - x = 10
4x + 2x -x =10 +3 +2
5x = 15
x = 15/5 = 3

(6)
0.18x - 11.65 = 0.41x - 9.58
-0.18x -0.18x

- 11.65 = 0.23x - 9.58
+9.58 +9.58

-2.07 = 0.23x
-2.07/0.23 = x
-9 = x

Answer 2

1. -2/3 + 3x = 1/3
+ 3x = 1/3 +2/3
+ 3x = 1
x = 1/3

2. 15m - 4 = 12m - 3m - 16
15m - 12m + 3m = - 16 +4
6m = - 12
m = - 12/6
m = - 2

3. 8r + 4(2r - 6) = 4r -4
8r -4r + 8r - 24 = -4
12r = -4 +24
r = +20/12
r = 1 8/12
r = 1 2/3

4. 3/5y + 2 = 8
3/5y = 8 -2
3y = (8 -2) x 5
3y = (6) x 5
3y = 30
y = 30/3
y = 10

5. 4x - 3 + 2x -2 - x = 10
4x + 2x - x = 10 + 3 + 2
5x = 15
x = 15/5
x = 3

6. 0.18x - 11.65 = 0.41x - 9.58
0.18x -0.41x = - 9.58 + 11.65
0.59x = -2.07
x = -2.07/0.59
x = -3.508475

Answer 3

1.) -2/3 + 3x = 1/3
Add 2/3 to both sides:
3x = 1/3 + 2/3
=> 3x = 1
=> x = 1/3

2.) 15m - 4 = 12m - 3m - 16
Put all the m terms on the left and the numbers on the right; remember to change sign from + to - or vice versa when you go from one side to the other.
15m - 12m + 3m = -16 + 4
=> (15 - 12 + 3) m = -12
=> 6m = -12
=> m = -12/6 = -2.

3.) 8r + 4(2r - 6) = 4r - 4
Expand the brackets:
8r + 4(2r) + 4(-6) = 4r - 4
=> 8r + 8r - 24 = 4r - 4
Now put r terms on the left and numbers on the right:
=> 8r + 8r - 4r = -4 + 24
=> 12r = 20
=> r = 20/12 = 5/3.

4.) 3/5y + 2 = 8
I assume this is (3/5)y rather than 3/(5y). But I'll work both for you just in case...
(3/5) y + 2 = 8
=> (3/5) y = 8-2 = 6
=> y = 6 ÷ 3/5
= 6 × 5/3
= 30/3 = 10.

3/(5y) + 2 = 8
=> 3/(5y) = 8-2 = 6 = 6/1
Cross-multiply to get
3(1) = 6(5y)
=> 3 = 30y
=> y = 1/10.

5.) 4x - 3 + 2x - 2 - x = 10
=> 4x + 2x - x = 10 + 3 + 2
=> (4+2-1) x = 15
=> 5x = 15
=> x = 15/5 = 3.

6.) 0.18x - 11.65 = 0.41x - 9.58
=> 0.18x - 0.41x = -9.58 + 11.65
=> (0.18 - 0.41) x = 2.07
=> -0.23 x = 2.07
=> x = 2.07 / (-0.23) = -9.

Answer 4

1) -2/3 + 3x = 1/3

3x = 1/3+ 2/3 = 1
x= 1/3

2) 15m-4 = 12m-3m-16

15m -12m + 3m= 4 -16
3m + 3m = 6m = -12
m= -12/6 = -2

3) 8r +4 (2r -6) = 4r-4
8r + 8r -24 = 4r-4
16r -4r = 24 - 4
12r = 20
r = 20/12 = 5/3

4)3/5y + 2 = 8
3/5y = 8 - 2 = 6
3 = 6 (5y) = 30 y
y = 3/30 = 1/10

5) 4x - 3 + 2x -2 -x = 10
4x + 2x -x = 5x = 10 +3+2= 15
x = 15/5 = 3




6) 0.18x -11.65 = 0.41x - 9.58

0.18x -0.41x = 11.65 -9.58 = - 0.23 x = 2.07
x = - 2.07/0.23 = -9

Answer 5

1.) -2/3 + 3x = 1/3 <-- Multiply by 3 getting:
-2 +9x =1
9x= 3
x = 1/3

2.) 15m - 4 = 12m - 3m - 16
15m -12m +3m = 4-16
6m = -12
m=-2

3.) 8r + 4(2r - 6) = 4r - 4
8r +8r -24 = 4r -4
8r+8r-4r = 24-4
12r = 20
r = 20/12 = 5/3

4.) 3/5y + 2 = 8
3/5y = 8-2 = 6
(5/3)(3/5)y = 5/3*6
y = 10

5.) 4x - 3 + 2x - 2 - x = 10
4x+2x-x = 10 +3+2
5x =15
x=3

6.) 0.18x - 11.65 = 0.41x - 9.58
18x -1165 =41x -958
18x -41x = 1165 -958
-23x = 207
x = 207/-23 = -9

Answer 6

1. Add 2/3 to both sides to isolate the 3x.
3x=2/3+1/3 (which sums to 1)
3x= 1, Then divide bothe sides by 3 to isolate the x
x=1/3
Check your answer by inputing x back into the equation.

-2/3+ 3(1/3)= 1/3
-2/3+ 3/3 =1/3
1/3 = 1/3 Correct x=1/3

2. 15m - 4 = 12m - 3m - 16
Get the m on on side and the numbers on the other.
Rewrite 15m-4= -16 + 12m -3m
15m-4=-16 + 9m Then subtract 9m from both sides and add 4 to reach
6m= -12 Divide by 6 for m
m= -2 Check your answer to by substituting m (be careful to which ones turn negative and which positive when substituting.

Answer 7

1.-2/3+3x=1/3
=> -2+9x=1 [multiplying all by 3]
=>9x=1+2=3
x=3/9=1/3 ans
2> 15m-4=12m-3m-16
=>15m-12m+3m= -16+4
=.6m=-12
m= -12/6= -2 ans
3.8r+4(2r-6)=4r-4
=>8r+8r-24=4r-4
=>8r+8r-4r= -4+24
=>12r=20
=r=20/12 =5/3= 1 2/3
4.3/5y +2=8
=>3/5y=8-2=6
=>30y=3 [ny cross-multiplication}
=>y=3/30=1/10 ans
5.4x-3+2x-2-x=10
=>5x-5=10
=>5x=10+5=15
=>x=15/5=3 ans
6.0.18x-11.65=0.41x-9.58
=>0.18x-0.41x= -9.58+11.65
=> -0.23x=2.07
x=2.07/-0.23= -9 ans.

Answer 8

Eloise, you have to remember the fundamentals. You have to collect like terms together. With these equations, the "like terms" are constants and terms with the variable. For example, in (1)
....move your constants to the right side and you have 3x = 1. Hmmm, that means x = 1/3. Right?

3. This is slightly harder because of the term in ( ).
But fundamentals tells you that you handle that first, so you get...... 8r + 8r -24 = 4r-4. Then proceed.

6. Should be no problem. Just handle the decimals correctly.

Answer 9

1.) -2/3 + 3x = 1/3 add 2/3 to each side
3x=1/3+2/3=1 divide both sides by 3
x=1/3

2.) 15m - 4 = 12m - 3m - 16 add 4 to each side
15m=9m-12 subtract 9m from each side
6m=-12 divide both sides by 6
m=-2

3.) 8r + 4(2r - 6) = 4r - 4 divide both sides by 4
2r+2r-6=r-1 subtract r from rach side
3r-6=-1 add 6 to each side
3r=5 divide both sides by 3
r=5/3

4.) 3/5y + 2 = 8
I think you mean (3/5)y subtract 2 from each side
(3/5)y=6 multiply both sides by 5/3
y=6(5/3)
y=10

5.) 4x - 3 + 2x - 2 - x = 10 combine like terms
5x-5=10 divide both sides by 5
x-1=2 add 1 to each side
x=3

6.) 0.18x - 11.65 = 0.41x - 9.58 add 11.65 to each side
0.18x=0.41x+2.07 subtract 0.41x from each side
-0.23x=2.07 divide both sides by -0.23
x=-9

Answer 10

all you have to do is bring the numbers to one side and the numbers with variables to the other. for ex:
1) -2/3 + 3x = 1/3
3x = 1/3 + 2/3 (don't forget that you add the opposite of the sign when bringing it to the other side)
3x = 1 (add it together)
x = 1/3 (divide the 3 from both sides)

thats the basic outline for what you have to do =]

I'll help you do the last one since it looks the hardest.

6) .18x - 11.65 = .41x - 9.58
.18x -.41x = 11.65 - 9.58 (i brought the x to one side)
.4x = 2.07 (divide the 4 from both sides)
x= 5.175