Lesson Vocabulary

• identity

Problem 1 Solving an Equation With Variables on Both Sides

What is the solution of 5x + 2 = 2x + 14?

5 x + 2 = 2 x + 14   5 x + 2 − 2 x = 2 x + 14 − 2 x Subtract  2 x  from each side . 3 x + 2 = 14 Simplify . 3 x + 2 − 2 = 14 − 2 Subtract  2  from each side . 3 x = 12 Simplify . 3 x 3 = 12 3 Divide each side by  3 . x = 4 Simplify . table with 7 rows and 3 columns , row1 column 1 , 5 x plus 2 , column 2 equals 2 x plus 14 , column 3 , row2 column 1 , 5 x plus 2 minus 2 x , column 2 equals 2 x plus 14 minus 2 x , column 3 cap subtract . 2 x . fromeachside . . , row3 column 1 , 3 x plus 2 , column 2 equals 14 , column 3 cap simplify , . , row4 column 1 , 3 x plus 2 minus 2 , column 2 equals 14 minus 2 , column 3 cap subtract . 2 . fromeachside . . , row5 column 1 , 3 x , column 2 equals 12 , column 3 cap simplify , . , row6 column 1 , fraction 3 x , over 3 end fraction , column 2 equals , 12 over 3 , column 3 cap divideeachsideby . 3 . , row7 column 1 , x , column 2 equals 4 , column 3 cap simplify , . , end table

Check

5 x + 2 = 2 x + 14 5 ( 4 ) + 2 = ? 2 ( 4 ) + 14 Substitute  4  for  x . 22 = 22   ✓ Simplify. The solution checks. table with 3 rows and 2 columns , row1 column 1 , 5 x plus 2 , column 2 equals 2 x plus 14 , row2 column 1 , 5 open 4 close plus 2 , column 2 modified equals with question mark above , 2 open 4 close plus 14 , column 3 cap substitute . 4 , for , x . , row3 column 1 , 22 , column 2 equals 22 check mark , column 3 cap simplify. cap the solution checks. , end table