Chapter 9 - XYZ Custom Plus

9.2 The Addition Property of Equality
525
Example 4
Solve for a: a 2 3 5 5
4. Solve for a: a 2 2 5 7
Solution a 2 3 5 5
a 2 3 1 3 5 5 1 3
a 1 0 5 8
a 5 8
Add 3 to both sides
Addition
a 1 0 5 a
The solution to a 2 3 5 5 is a 5 8.
Example 5
Solve for y: y 1 4 2 6 5 7 2 1
5. Solve for y: y 1 6 2 2 5 8 2 9
Solution
Before we apply the addition property of equality, we must simplify
each side of the equation as much as possible:
y 1 4 2 6 5 7 2 1
y 2 2 5 6
y 2 2 1 2 5 6 1 2
y 1 0 5 8
y 5 8
Simplify each side
Add 2 to both sides
Addition
y 1 0 5 y
Example 6
Solve for x: 3x 2 2 2 2x 5 4 2 9
6. Solve for x: 5x 2 3 2 4x 5 4 2 7
Solution
Simplifying each side as much as possible, we have
3x 2 2 2 2x 5 4 2 9
x 2 2 5 25
x 2 2 1 2 5 25 1 2
x 1 0 5 23
x 5 23
3x 2 2x 5 x
Add 2 to both sides
Addition
x 1 0 5 x
Example 7
Solve for x: 23 2 6 5 x 1 4
7. Solve for x: 25 2 7 5 x 1 2
Solution
The variable appears on the right side of the equation in this problem.
This makes no difference; we can isolate x on either side of the equation. We
can leave it on the right side if we like:
23 2 6 5 x 1 4
29 5 x 1 4 Simplify the left side
29 1 (−4) 5 x 1 4 1 (−4) Add 24 to both sides
213 5 x 1 0 Addition
213 5 x x 1 0 5 x
The statement 213 5 x is equivalent to the statement x 5 213. In either case the
solution to our equation is 213.
Example 8
Solve: a 2 3 } 4
5 5 } 8
8. Solve: a 2 } 2 3 } 5 }5 6 }
Solution
To isolate a we add } 3 } to each side:
4
a 2 3 } 4
5 5 } 8
a 2 3 } 4
1 3 − 4
5 5 } 8
1 3 − 4
a 5 11 } 8
When solving equations we will leave answers like } 1 81 } as improper fractions,
rather than change them to mixed numbers.
Answers
4. 9 5. 25 6. 0 7. 214
8. } 3 2 }