SOLUTION: how do you solve 4(m+3)+7=4m+19

Question 220325: how do you solve 4(m+3)+7=4m+19
Found 2 solutions by rapaljer, jim_thompson5910:
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
4(m+3)+7=4m+19
4m+12+7=4m+19
4m+19=4m+19

Now, if you continue to solve for m, you will probably subtract 4m from each side, and there will be NO variables left. This leaves 19=19, which is ALWAYS true! Notice that 4m+19 ALWAYS EQUALS 4m+19. We call this an IDENTITY, and the solution is ALL REAL NUMBERS, since any value of m would make the statement true.

See also my own non-traditional explanation of this topic on my own website. Do a "Bing" search for my last name "Rapalje". Look for "Rapalje Homepage" near the top of the search list. Near the top of my Homepage, look for "Basic, Intermediate and College Algebra: One Step at a Time." Choose "Basic Algebra", look for "Chapter 1". Your particular problem here relates to my section called "Section 1.08 Equation Solving." This section is also supplemented by the corresponding section of "MATH IN LIVING COLOR". I think I hava a LOT of resources available FREE on this website. Let me know if you need help finding anything!!

R^2

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation.

Distribute.

Combine like terms on the left side.

Subtract from both sides.

Subtract from both sides.

Combine like terms on the left side.

Combine like terms on the right side.

Simplify.

Since this equation is always true for any m value, this means m can equal any number.

So there are an infinite number of solutions.

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