Question

Which of the following equations have the same solution? Solve all three equations separately and explain each step.

Answer 1

One moment, putting it up

Answer 2

I. 2x + 4 = 3x – 11
II. 3x + 3 = 51
III. \[\frac{ 2x + 1 }{ 3 } = \frac{ x + 6 }{ 2 }\]

Answer 3

I.

Solve for x:
2 x+4 = 3 x-11
Subtract 3 x from both sides:
(2 x-3 x)+4 = (3 x-3 x)-11
2 x-3 x = -x:
-x+4 = (3 x-3 x)-11
3 x-3 x = 0:
4-x = -11
Subtract 4 from both sides:
(4-4)-x = -11-4
4-4 = 0:
-x = -11-4
-11-4 = -15:
-x = -15
Multiply both sides of -x = -15 by -1:
(-x)/(-1) = 15
(-1)/(-1) = 1:
Answer
x = 15

Answer 4

II.

Solve for x:
3 x+3 = 51
Subtract 3 from both sides:
3 x+(3-3) = 51-3
3-3 = 0:
3 x = 51-3
51-3 = 48:
3 x = 48
Divide both sides of 3 x = 48 by 3:
(3 x)/3 = 48/3
3/3 = 1:
x = 48/3
The gcd of 48 and 3 is 3, so 48/3 = (3\[Times]16)/(3\[Times]1) = 3/3\
\[Times]16 = 16:
Answer:
x = 16

Answer 5

III.

Solve for x:
(2 x+1)/3 = (x+6)/2
Multiply both sides by 6:
(6 (2 x+1))/3 = (6 (x+6))/2
6/3 = (3*2)/3 = 2:
2 (2 x+1) = (6 (x+6))/2
6/2 = (2*3)/2 = 3:
2 (2 x+1) = 3 (x+6)
Expand out terms of the left hand side:
4 x+2 = 3 (x+6)
Expand out terms of the right hand side:
4 x+2 = 3 x+18
Subtract 3 x from both sides:
(4 x-3 x)+2 = (3 x-3 x)+18
4 x-3 x = x:
x+2 = (3 x-3 x)+18
3 x-3 x = 0:
x+2 = 18
Subtract 2 from both sides:
x+(2-2) = 18-2
2-2 = 0:
x = 18-2
18-2 = 16:
Answer:
x = 16

Answer 6

II and III have the same solution.

Answer 7

@half I see... thank you for the help!