2-5 Addition Equations

Learn to solve whole-number addition equations.

2-5 Addition Equations

inverse operations

Vocabulary

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 68To rebalance the scale, take away 14 from the other side.

h + 14 82

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 –14h = 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.

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 – 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.

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 –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.

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 – 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.

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 –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.

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 –12

83 = d

12 is added to d.

Subtract 12 from both sides to undo the addition.

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 –17

18 = d

17 is added to d.

Subtract 17 from both sides to undo the addition.