Equations and Inequalities

Unit 8 – Solving Addition and Subtraction Equations Algebraically

Vocabulary Isolate – to set apart. Inverse Operation – an operation that is the opposite of, or undoes, another operation; addition and subtraction are inverse operations; multiplication and division are inverse operations.

Solving Subtraction Equations Algebraically - Example Solve algebraically for x , then check. Solve x – 12 = 23 + 12 + 12 x = 35 We added 12 to both sides because there was a -12 on the same side as the x and you do the opposite to eliminate (get rid of) a term. Check x – 12 = 23 (35) – 12 = 23 23 = 23 If the final line is correct, you have the right value for x. If it is not correct, go back to the work you did to solve for x and start again.

Solving Subtraction Equations Algebraically - Example Solve algebraically for x , then check. Solve x – 15 = 47 + 15 + 15 x = 62 Check x – 15 = 47 (62) – 15 = 47 47 = 47

Solving Addition Equations Algebraically - Example Solve algebraically for x , then check. Solve x + 25 = 139 _- 25 - 25 x = 114 Check x + 25 = 139 (114) + 25 = 139 139 = 139

Solving Addition Equations Algebraically - Example Solve algebraically for x , then check. Solve 34 + x = 42 34 + x = 42 - 34 - 34 x = 8 Check 34 + x = 42 34 + (8) = 42 42 = 42

Solving Addition & Subtraction Equations Algebraically - Practice Solve algebraically, then check. y + 13 = 84 y = 71 z – 14 = 54 z = 68 3. 6 + t = 55 t = 49 u – 24 = 82 u = 106

More Solving Addition & Subtraction Equations Algebraically - Practice Solve algebraically, then check. y + 12.6 = 24.39 y = 11.79 z – 2 1 4 = 3 3 5 z = 5 17 20 14.86 = t – 8.3 t = 23.16 15 3 4 = u + 8 1 3 u = 7 5 12