SOLUTION: Ref. Questions 1043754, 1043749: d(a + x) - b(c - x) = da da + dx - bc + bx = da da - da + dx - bc + bx dx - bc + bx ??

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Question 1043756: Ref. Questions 1043754, 1043749:
d(a + x) - b(c - x) = da
da + dx - bc + bx = da
da - da + dx - bc + bx
dx - bc + bx
??
Answer by josgarithmetic(39628) About Me  (Show Source):
You can put this solution on YOUR website!
PROPERTIES OF NUMBERS; PROPERTIES OF EQUALITY; COMBINING LIKE TERMS; ISOLATING THE VARIABLE; FACTORING

You need to learn these, and apply them in problem-solving. Isolate the variable to be solved. Undo what has been done to the variable so you can isolate it and solve for it.

What is stopping you? What exactly do you not understand? If someone gives you the justification for each step, can you write the step? What you should really, REALLY do, is study all of your Algebra 1 course up to your current section or lesson so that you really learn these needed number properties.

What if someone gives each step but leaves all of the simplifications until last? Let's try that!

d%28a%2Bx%29-b%28c-x%29=da
-
da%2Bdx-%28bc-bx%29=da
da%2Bdx-bc%2Bbx=da
da-da%2Bdx-bc%2Bbx=0
dx%2Bbx-bc%2Bda-da=0
%28d%2Bb%29x-bc%2Bda-da=0
%28d%2Bb%29x-bc%2Bda-da%2Bbc-da%2Bda=bc-da%2Bda
%28d%2Bb%29x=bc-da%2Bda
%28d%2Bb%29x%281%2F%28d%2Bb%29%29=%28bc-da%2Bda%29%281%2F%28d%2Bb%29%29
x=%28bc%29%2F%28d%2Bb%29

Do you know WHY each step works? Can you recognize that the variable, x, was isolated using inverse properties, and that most of the simplifications were done at or near the end of the sequence of steps?