math
posted by Abby
could someone check my work please? I have to solve for 'x'
Questions ~
1. 3x – 19 = 2
Add ‘19’ to each side of the equation ~ 19+19+3x= 2+19
Combine like terms~ 19+19=0
0+3x= 2+19
3x= 2+19
Combine like terms~ 2+19=17
3x=17
Divide each side by‘3’~ x=5.666666667
X = 5.666666667
2. 4x  12x = 62 + 4(11)
Combine like terms ~ 4x+12x=8x
8x= 62+4(11)
Multiply ~ 4*11
8x=62+44
Combine like terms ~ 62+44=106
8x=106
Divide each side by ‘8’ X=13.25
X= 13.25
3. x/8 + 7 =  10
?? I can't figure this out
4. 4(5x – 9) = 2(3x + 7)
Add ‘6x’to each side of the equation ~ 36+20x+6x= 14+ 6x+6x
Combine like terms ~ 20x +6x=26x
36+26x=14+ 6x+6x
Combine like terms ~ 6x+6x=0
36+26x= 14+0
36+26=14
Add ‘36’ to each side of the equation ~ 36+36+26x=14+36
Combine like terms ~ 36+36=0
0+26x= 14+36
26x= 14+36
Combine like terms ~ 14+36=22
26x=22
Divide each side by ‘26’ ~ x= 0.8461538462
x= 0.8461538462
5. ½ x – 5 = (3/8)x + 2
?? I can't figure this one out
6. 3(x – 4) – (x + 5) = 2x + 11
Combine like terms ~ 12+ 5= 17
17+3x+ 1x=2x+11
Combine like terms ~ 3x+ 1x=2x
17+2x=2x+11
Add ‘2x’ to each side of the equation
17+2x+2x=11+2x+2x
Combine like terms~ 2x+ 2x=0
17+0=11+2x+2x
17=11+2x+2x
Combine like terms~ 2x+ 2x=0
17+11+0
17=11
I think I did something wrong with question #6 but I can’t figure out what it is, could someone help me figure it out?
Questions #3 and #5 I couldn’t figure out how to do them, I would really appreciate any help you could give.
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Reiny
all your questions are correct, except the two you could not do
first of all, let's clear up that last one.
you ended up with 17 = 11
This of course is false even though you made no errors in your solution.
If that happens , and you end up with an absurd conclusion like that, simply say:
There is no solution to that equation
In general,
 if your variables drop out and you end up with a false statement, there is no solution
 if your variables drop out and you end up with a true statement, such as 17 = 17, any real value of the variable would be a solution.
Such an equation is called an identity,
e.g. 2x + 4 = 2x + 6  2
#3
x/8 + 7 = 10
x/8 = 17
multiply both sides by 8, cancelling the 8 on the left side
x = 136
#5
½ x – 5 = (3/8)x + 2
I see 4 terms, the LCM of my two denominators is 8
how about multiplying every term by 8 ?
4x  40 = 3x + 16
hey look ma, no more fractions !
4x + 3x = 16+40
7x = 56
x = 56/7 = 8
one more comment.
Unless your decimals come out exact, I would consider the corresponding fraction to be in better and proper form
e.g #1, leave it as 17/3 rather than 5.666667
and 22/26 as 11/13 instead of the repeating decimal 
Abby
Alright! thank you so much! this really helps!
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could someone check my work please? I have to solve for 'x' Questions ~ 1. 3x – 19 = 2 Add ‘19’ to each side of the equation ~ 19+19+3x= 2+19 Combine like terms~ 19+19=0 0+3x= 2+19 3x= 2+19 Combine like terms~ 2+19=17