Page 180 - Algebra 1

Example
1
Using Inverse Operations
Solve 6x = 4x - 10. Justify each step. Check the solution. SOLUTION
Math Language
Inverse operations
undo each other. Addition and subtraction are inverse operations. Multiplication and division are inverse operations.
6x = 4x - 10 -_4_x = -_4_x
x = -5
Check Substitute-5forxintheoriginalequation.
6x = 4x - 10 6(-5) 4(-5) - 10 -30 -20 - 10
-30 = -30 ✓
Equations with variables on both sides might also contain symbols of inclusion and like terms. The first step is to apply the Distributive Property. The second step is to add like terms. Then apply inverse operations and the properties of equality to solve the equation.
Simplifying Before Solving
Solve 5(2x + 4) - 2x = 6 + 2(3x + 12). Justify each step. SOLUTION
5(2x+4)-2x= 6+2(3x+12)
2x = -10 2x = -10
Subtraction Property of Equality Combine like terms.
Division Property of Equality
__ 22
Example
2
10x + 20 - 2x 10x - 2x + 20 8x + 20
-_ 6 _ x
2x + 20
-_ 2 _ 0 2x
= 6+6x+24 = 6x+6+24 = 6x + 30
= -_ 6 _ x
= 30 = -_ 2 _ 0 = 10
Distributive Property Commutative Property Combine like terms. Subtraction Property of Equality Simplify.
Subtraction Property of Equality Simplify.
Multiplication Property of Equality
Simplify.
Math Reasoning
Write What is another way to eliminate the coefficient 2 from 2x?
_1 · 2 x = 1 0 · _1 22
x=5
An identity is an equation that is always true. It has infinitely many solutions. If no value of the variable makes an equation true, then the equation has no solution.
Lesson 28 165