5-5 Solving x + a = b
Objectives:
1. Solve equations of the form x + a = b
2. Recognize uses of the commutative and associative properties of addition and the addition property of equality.
Big Idea : An equation of the form x + a = b can be solved by adding –a to both of its sides.
Equation of the form x + a = b . x is a variable and a and b are numbers. ex: x + 3 = 7
Addition property of equality
– for all real number a, b and c if a = b then a + c = b + c or in
English if two values are equal then you can add anything you want to both values and the sums will be equal also. Used in solving equations.
Steps to solve addition equations
1. Rewrite the original
2. Simplify on both sides of the equal sign first (if possible)
3. Use the Addition Property of Equality to undo what they did to the variable.
4. Simplify using the property of opposites, Identity Property of Addition and arithmetic
5. Check solution in original.
Example: Solve 10.6 = -5.2 + n and give the property or reason for each step.
10.6 = -5.2 + n Original
5.2 + 10.6 = -5.2 + 5.2 + n Addition Property of Equality
5.2 + 10.6 = 0 + n Property of Opposites
5.2 + 10.6 = n
15.8 = n
Identity Property of Addition
Artithmetic
Check: 10.6 = -5.2 + 15.8
10.6 = 10.6
When solving equations, each step is written underneath the previous step with equal signs lined up.
EX: Solve 29 + a – 6 = -4
29
 a

6
 
4 check:
29
 a
 
6
 
4
23
 a
 
4
23
 
23
 a
 
4
 
23 a
 
27
29
 
27

6
 
4
2
 
6
 
4

4
 
4
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