1). x in (-oo:+oo)
(1/3)*(x-15) = 2/3 // - 2/3
(1/3)*(x-15)-(2/3) = 0
(1/3)*(x-15)-2/3 = 0
1/3*(x-15)-2/3 = 0
(1/3*3*(x-15))/3-2/3 = 0
1/3*3*(x-15)-2 = 0
x-17 = 0
(x-17)/3 = 0
(x-17)/3 = 0 // * 3
x-17 = 0
x-17 = 0 // + 17
x = 17
x = 17
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2). Simplifying
3X + 1 = 3x + 5
Reorder the terms:
1 + 3X = 3x + 5
Reorder the terms:
1 + 3X = 5 + 3x
Solving
1 + 3X = 5 + 3x
Solving for variable 'X'.
Move all terms containing X to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + 3X = 5 + -1 + 3x
Combine like terms: 1 + -1 = 0
0 + 3X = 5 + -1 + 3x
3X = 5 + -1 + 3x
Combine like terms: 5 + -1 = 4
3X = 4 + 3x
Divide each side by '3'.
X = 1.333333333 + x
Simplifying
X = 1.333333333 + x
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3). 12x=7x+5x
We move all terms to the left:
12x-(7x+5x)=0
We add all the numbers together, and all the variables
12x-(+12x)=0
We get rid of parentheses
12x-12x=0
We add all the numbers together, and all the variables
=0
x=0/1
x=0
(hope that helps you out)