Page 168 - Algebra 1

LESSON Solving Multi-Step Equations 26
Warm Up
New Concepts
1. Vocabulary The product of a number and its (11)
2. Simplify 2x + 5y + 3x - 2y by adding like terms. (18)
3. Solve 2x + 5 = 12. Check your solution. (23)
4. Multiple Choice Which is the solution of 3x + 6 = 33?
(23)
is 1.
A 13 B 9 C7 D8
Equations that are more complex may have to be simplified before they can be solved. More than two steps may be required to solve them. If there are like terms on one side of an equation, combine them first. Then apply inverse operations and the properties of equality to continue solving the equation.
Combining Like Terms
Solve 5x + 8 - 3x + 2 = 20. Justify each step. Check the solution.
Example
1
SOLUTION
5x + 8 - 3x + 2 = 20 5x - 3x + 8 + 2 = 20 2x + 10 = 20
-_ 1 _ 0 = -_ 1 _ 0
2x = 10
2x = 10 __
22 x=5
Check Substitute5forx.
5x + 8 - 3x + 2 = 20 5(5) + 8 - 3(5) + 2 20 25 + 8 - 15 + 2 20
Commutative Property of Addition Combine like terms.
Subtraction Property of Equality Simplify.
Division Property of Equality Simplify.
Math Language
Like terms have the same variable(s) raised to the same power(s).
Online Connection www.SaxonMathResources.com
20=20 ✓
Complex equations can contain symbols of inclusion such as parentheses and brackets. Eliminate the symbols of inclusion first. Use the Distributive Property if multiplication is indicated by the symbols of inclusion. Then combine like terms on each side of the equation. Continue to solve the equation by applying inverse operations and the properties of equality.
Lesson 26 153