1. 2-5 Addition Equations Learn to solve whole-number addition equations.

2. 2-5 Addition Equations inverse operations Vocabulary

3. 2-5 Addition Equations The equation h + 14 = 82 can be represented as a balanced scale. h + 14 82 To find the value of h, you need h by itself on one side of the scale. h ? To get h by itself, first take away 14 from the left side of the scale. Now the scale is unbalanced. h 68 To rebalance the scale, take away 14 from the other side. h + 14 82

4. 2-5 Addition Equations Taking away 14 from both sides of the scale is the same as subtracting 14 from both sides of the equation. h + 14 = 82 –14 h = 68 Inverse operations undo each other. Addition and subtraction are inverse operations. If an equation contains addition, solve it by subtracting from both sides to “undo” the addition.

5. 2-5 Addition Equations Solve the equation. Check your answer. Additional Example 1A: Solving Addition Equations x + 87 = 152 Check x + 87 = 152 x + 87 = 152 87 is added to x. x = 65 – 87 Subtract 87 from both sides to undo the addition. 65 + 87 = 152 ? 152 = 152 ? Substitute 65 for x in the equation. 65 is the solution.

6. 2-5 Addition Equations Solve the equation. Check your answer. Additional Example 1B: Solving Addition Equations 72 = 18 + y Check 72 = 18 + y 72 = 18 + y 18 is added to y. 54 = y –18 Subtract 18 from both sides to undo the addition. 72 = 18 + 54 ? 72 = 72 ? Substitute 54 for y in the equation. 54 is the solution.

7. 2-5 Addition Equations Solve the equation. Check your answer. Check It Out: Example 1A u + 43 = 78 Check u + 43 = 78 u + 43 = 78 43 is added to u. u = 35 – 43 Subtract 43 from both sides to undo the addition. 35 + 43 = 78 ? 78 = 78 ? Substitute 35 for u in the equation. 35 is the solution.

8. 2-5 Addition Equations Solve the equation. Check your answer. Check It Out: Example 1B 68 = 24 + g Check 68 = 24 + g 68 = 24 + g 24 is added to g. 44 = g –24 Subtract 24 from both sides to undo the addition. 68 = 24 + 44 ? 68 = 68 ? Substitute 44 for g in the equation. 44 is the solution.

9. 2-5 Addition Equations Johnstown, Cooperstown, and Springfield are located in that order in a straight line along a highway. It is 12 miles from Johnstown to Cooperstown and 95 miles from Johnstown to Springfield. Find the distance d between Cooperstown and Springfield. Additional Example 2: Social Studies Application It is 83 miles from Cooperstown to Springfield. 95 = 12 + d distance between Johnstown and Springfield distance between Johnstown and Cooperstown distance between Cooperstown and Springfield = + 95 = 12 + d –12 83 = d 12 is added to d. Subtract 12 from both sides to undo the addition.

10. 2-5 Addition Equations Patterson, Jacobsville, and East Valley are located in that order in a straight line along a highway. It is 17 miles from Patterson to Jacobsville and 35 miles from Patterson to East Valley. Find the distance d between Jacobsville and East Valley. Check It Out: Example 2 It is 18 miles from Jacobsville to East Valley. 35 = 17 + d distance between Patterson and East Valley distance between Patterson and Jacobsville distance between Jacobsville and East Valley = + 35 = 17 + d –17 18 = d 17 is added to d. Subtract 17 from both sides to undo the addition.