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.
Multiply both sides by 8.
3. x + 56 = -80
5. 4x - 40 = -3x +16
6. Get rid of parentheses.
3x - 12 - x - 5 = 2x + 11
Combine like terms and solve for x.
However, unless you have a typo, #6 is unsolvable.
I'd be happy to help you with your work. Let's go through each of the questions:
1. 3x – 19 = -2
To solve for x, we need to isolate the variable x. We can do this by performing operations on both sides of the equation to get rid of any constants or coefficients.
First, add 19 to both sides:
3x - 19 + 19 = -2 + 19
This simplifies to:
3x = 17
Now, divide both sides by 3 to solve for x:
3x/3 = 17/3
This gives us:
x = 5.666666667
2. 4x - 12x = 62 + 4(11)
Combine like terms on the left side:
-8x = 62 + 44
Simplify the right side:
-8x = 106
Now, divide both sides by -8:
x = -13.25
3. x/8 + 7 = -10
To solve for x, we need to isolate x on one side of the equation. Start by subtracting 7 from both sides:
x/8 = -10 - 7
Simplify the right side:
x/8 = -17
Next, multiply both sides by 8 to get rid of the fraction:
8(x/8) = -17 * 8
Simplifying further, we have:
x = -136
4. 4(5x – 9) = -2(3x + 7)
Expand the parentheses on both sides:
20x - 36 = -6x - 14
Combine like terms:
20x + 6x = -14 + 36
Simplify further:
26x = 22
Finally, divide both sides by 26:
x = 0.8461538462
5. ½ x – 5 = (-3/8)x + 2
To solve for x, we want to eliminate any fractions. Multiply both sides by the least common denominator (in this case, 8) to clear the fractions:
8 * (1/2)x - 8 * 5 = 8 * (-3/8)x + 8 * 2
This simplifies to:
4x - 40 = -3x + 16
Now, combine like terms:
4x + 3x = 16 + 40
Simplify further:
7x = 56
Finally, divide both sides by 7:
x = 8
6. 3(x – 4) – (x + 5) = 2x + 11
Distribute the 3 on the left side and the -1 on the right side:
3x - 12 - x - 5 = 2x + 11
Combine like terms:
2x - 17 = 2x + 11
Now, subtract 2x from both sides to isolate the x terms:
2x - 2x - 17 = 2x - 2x + 11
Simplifying further:
-17 = 11
This equation leads to a contradiction, which means there is no solution for x.
I hope that helps! Let me know if you have any further questions.