# 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.

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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

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2. Alright! thank you so much! this really helps!

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