Think

How is this equation different from equations you've seen before?

The variable occurs in two terms. You can simplify the equation by grouping like terms and combining them.

Problem 1 Combining Like Terms

What is the solution of 5 = 5 m − 23 + 2 m ? equals 5 bold italic m minus 23 plus 2 bold italic m question mark

5 = 5 m − 23 + 2 m   5 = 5 m + 2 m − 23 Commutative Property of Addition 5 = 7 m − 23 Combine like terms . 5 + 23 = 7 m − 23 + 23 Add  23  to each side . 28 = 7 m Simplify . 28 7 = 7 m 7 Divide each side by  7 . 4 = m Simplify . table with 7 rows and 3 columns , row1 column 1 , 5 , column 2 equals 5 m minus 23 plus 2 m , column 3 , row2 column 1 , 5 , column 2 equals 5 m plus 2 m minus 23 , column 3 cap commutativecap propertyofcap addition , row3 column 1 , 5 , column 2 equals 7 m minus 23 , column 3 cap combineliketerms . . , row4 column 1 , 5 plus 23 , column 2 equals 7 m minus 23 plus 23 , column 3 cap add , 23 . toeachside . . , row5 column 1 , 28 , column 2 equals 7 m , column 3 cap simplify , . , row6 column 1 , 28 over 7 , column 2 equals , fraction 7 m , over 7 end fraction , column 3 cap divideeachsideby . 7 . , row7 column 1 , 4 , column 2 equals m , column 3 cap simplify , . , end table

Check 5 = 5 m − 23 + 2 m 5 = ? 5 ( 4 ) − 23 + 2 ( 4 ) Substitute  4  for  m . 5 = 5 ✓ Simplify. The solution checks . table with 3 rows and 1 column , row1 column 1 , 5 equals 5 m minus 23 plus 2 m , row2 column 1 , 5 , modified equals with question mark above , 5 open 4 close minus 23 plus 2 open 4 close , column 2 cap substitute . 4 , for , m . , row3 column 1 , 5 equals 5 check mark , column 2 cap simplify. cap the solution checks . . , end table