# math

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.

1. 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

posted by Reiny
2. Alright! thank you so much! this really helps!

posted by Abby

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