Answer:
-1
Explanation:
You want the value of x that is a solution to 3x − 10x + 5 = 5x + 17.
Solution
It can be convenient to subtract the left side of the equation from both sides:
(3x -10x +5) -(3x -10x +5) = (5x +17) -(3x -10x +5) . . . . subtract (3x -10x +5)
0 = (5 -3 +10)x +(17 -5) . . . . . group like terms
0 = 12x +12 . . . . . . . . . . . simplify
0 = x +1 . . . . . . . . . . . divide by 12
-1 = x . . . . . . . . . . . subtract 1
The value of x that makes the equation true is -1.
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Additional comment
You might be told to solve this by simplifying it first to -7x+5 = 5x+17. This is recognizable as a 3-step equation, which might ordinarily be solved by the 3 steps ...
- subtract 5x ⇒ -12x +5 = 17
- subtract 5 ⇒ -12x = 12
- divide by -12 ⇒ x = -1
The first two steps can be combined to "subtract (5x+5)". The result is a negative coefficient on x. That coefficient could be positive by "add (7x-17)" instead, to get -12 = 12x.