Page 136 - Algebra 1

Exploration Using Inverse Operations
Copy and complete each table. Find the value of x by using the given values for the expression. Then explain how you found the values in the first column.
a.
x
60 _
x
1
2
3
4
5
6
x
4x
8
20
32
36
48
60
b.
c. Justify Is 20 a solution of the equation _60 = 3? Explain. x
d. Justify Is 7 a solution of the equation 4x = 54? Explain. Solving Equations by Multiplying
Example
1
Solve each equation. Then check the solution.
a. _x=8 b. -11=_1w 64
Hint
Inverse operations “undo” each other. Multiplying by 6 “undoes” dividing
by 6.
SOLUTION
_x = 8 6
6 · _x = 8 · 6 6
Multiplication Property of Equality
SOLUTION
_4 · -11 = _4 · _1w 1 1 4
-44 = w
Multiplication Property of Equality
Simplify.
Math Reasoning
Verify Show that dividing both sides of the equation by 5 or multiplying both sides of the equation by _1 , will
5
result in the same solution.
Check Substitute-44forw.
- 1 1 = _1 w 4
- 1 1 _1 ( - 4 4 ) 64
x = 48
Check Substitute6forx.
_
4 8 8
8=8 ✓
-11 = -11 ✓
Lesson 21 121