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.
Answer this Question
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
Alright! thank you so much! this really helps!
Sure! I'll be happy to help you with your questions.
Question 3: x/8 + 7 = -10
To solve this equation for 'x', we need to isolate the variable on one side of the equation. Here's how you can do it:
1. Start by subtracting 7 from both sides of the equation:
x/8 = -10 - 7
x/8 = -17
2. To get rid of the fraction division, we can multiply both sides of the equation by 8:
8 * (x/8) = -17 * 8
x = -136
Therefore, the solution to this equation is x = -136.
Question 5: 1/2 x - 5 = (-3/8)x + 2
To solve this equation for 'x', we can follow these steps:
1. Start by simplifying both sides of the equation:
Multiply both sides of the equation by 8 to get rid of the fraction:
8 * (1/2 x - 5) = 8 * ((-3/8)x + 2)
4x - 40 = -3x + 16
2. Combine like terms by adding 3x to both sides of the equation:
4x + 3x - 40 = -3x + 3x + 16
7x - 40 = 16
3. Add 40 to both sides of the equation:
7x - 40 + 40 = 16 + 40
7x = 56
4. Finally, divide both sides of the equation by 7 to solve for 'x':
(7x)/7 = 56/7
x = 8
Therefore, the solution to this equation is x = 8.
Now let's take a look at question 6 to figure out what went wrong.
Question 6: 3(x - 4) - (x + 5) = 2x + 11
Here's how you can solve this equation correctly:
1. Start by applying the distributive property:
3x - 12 - x - 5 = 2x + 11
2. Combine like terms by subtracting x and 5 from both sides of the equation:
3x - x - 12 - 5 = 2x + 11 - x - 5
2x - 17 = x + 6
3. Subtract x from both sides of the equation:
2x - x - 17 = x + 6 - x
x - 17 = 6
4. Add 17 to both sides of the equation:
x - 17 + 17 = 6 + 17
x = 23
So, the correct solution to this equation is x = 23.
I hope this helps! If you have any more questions or need further clarification, feel free to ask.