Could someone help me solves these questions? And can you show me how you did it? I can't figure out how to do these ones... I would really appreciate any help.
Questions~~
~ 3x – 19 = -2
~ 4x - 12x = 62 + 4(11)
~ x/8 + 7 = - 10
~ 4(5x – 9) = -2(3x + 7)
~ ½ x – 5 = (-3/8)x + 2
~ 3(x – 4) – (x + 5) = 2x + 11
If you show us how you would do the first problem, we can help you with the others.
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
Good.
What about the others?
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
Could you please show me how to do #3 and #5?
Sure, I'd be happy to help you solve these equations and show you how to do it. Let's go through each question step by step:
1. 3x – 19 = -2
To solve this equation, we want to isolate the variable x. First, let's add 19 to both sides of the equation to eliminate the -19 on the left side:
3x - 19 + 19 = -2 + 19
3x = 17
Next, divide both sides of the equation by 3 to solve for x:
(3x)/3 = 17/3
x = 17/3
So the solution for this equation is x = 17/3.
2. 4x - 12x = 62 + 4(11)
We can start by simplifying both sides of the equation:
-8x = 62 + 44
-8x = 106
Next, divide both sides of the equation by -8:
(-8x)/-8 = 106/-8
x = -13.25
So the solution for this equation is x = -13.25.
3. x/8 + 7 = -10
To isolate the variable x, let's begin by subtracting 7 from both sides of the equation:
x/8 + 7 - 7 = -10 - 7
x/8 = -17
Next, multiply both sides of the equation by 8 to solve for x:
8(x/8) = -17(8)
x = -136
So the solution for this equation is x = -136.
4. 4(5x – 9) = -2(3x + 7)
First, we will distribute the numbers inside the parentheses:
20x - 36 = -6x - 14
Next, let's combine like terms by moving all the x terms to one side and all the constant terms to the other side:
20x + 6x = -14 + 36
26x = 22
Finally, divide both sides of the equation by 26:
(26x)/26 = 22/26
x = 11/13
So the solution for this equation is x = 11/13.
5. ½ x – 5 = (-3/8)x + 2
Let's start by multiplying both sides of the equation by 8 to eliminate the fraction:
8(1/2 x – 5) = 8(-3/8)x + 2(8)
4x - 40 = -3x + 16
Next, combine like terms by moving all the x terms to one side and all the constant terms to the other side:
4x + 3x = 16 + 40
7x = 56
Finally, divide both sides of the equation by 7:
(7x)/7 = 56/7
x = 8
So the solution for this equation is x = 8.
6. 3(x – 4) – (x + 5) = 2x + 11
First, distribute the numbers inside the parentheses:
3x - 12 - x - 5 = 2x + 11
Next, combine like terms:
2x - 17 = 2x + 11
Notice that the variable terms cancel each other out. This means that the equation has no solution. It can be written as: 0 = 28, which is untrue.
Therefore, the equation has no solution.
I hope this explanation helps! Let me know if you have any further questions.