Page 169 - Algebra 1

Using Distributive Property
Solve x + 3(2x + 4) = 47. Justify each step. Check the solution.
Example
2
SOLUTION
x + 3(2x + 4) = 47 x + 6x + 12 = 47 7x + 12 = 47
-_ 1 _ 2 = -_ 1 _ 2
7x = 35
7x = 35 __
77 x=5
Check Substitute5forx.
x + 3(2x + 4) = 47 5 + 3[2(5) + 4] 47 5 + 3[10 + 4] 47 5 + 3[14] 47
47=47 ✓
When equations contain symbols of inclusion and like terms, first apply the Distributive Property. Next, add like terms. Then apply inverse operations and the properties of equality to solve the equation.
Simplifying before Solving
Solve 5x - (x - 3) - 1 = 18. Justify each step. Check the solution.
Distributive Property
Combine like terms. Subtraction Property of Equality Simplify.
Division Property of Equality Simplify.
Math Reasoning
Write What is another way to eliminate the coefficient 7 from 7x?
Example
3
SOLUTION
5x - (x - 3) - 1 = 18 5x - x + 3 - 1 = 18 4x + 2 = 18
-_ _2 = -_ _2 4x = 16
_1 · 4 x = 1 6 · _1 44
x=4 Check Substitute4forx.
5x - (x - 3) - 1 = 18 5(4) - (4 - 3) - 1 18 20 - 1 - 1 18
18=18 ✓
Distributive Property
Combine like terms. Subtraction Property of Equality Simplify.
Multiplication Property of Equality Simplify.
Caution
Remember to multiply by -1 when distributing a negative across parentheses.
154 Saxon Algebra 1