By Barbara Jund
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Additional resources for Algebra success in 20 minutes a day
Simplify both sides of the equation. 5x + 3 = 3x + 15 5x + 3 – 3 = 3x + 15 – 3 5x = 3x + 12 5x – 3x = 3x – 3x + 12 2x = 12 2x 12 ᎏ ᎏ = ᎏᎏ 2 2 x=6 Example: 4x + 6 = –2(3x + 4) Use the distributive property. Subtract 6 from both sides of the equation. Simplify both sides of the equation. Add 6x to both sides of the equation. Simplify both sides of the equation. Divide both sides of the equation by 10. Simplify both sides of the equation. 4x + 6 = –6x – 8 4x + 6 – 6 = –6x – 8 – 6 4x = –6x – 14 4x + 6x = –6x + 6x – 14 10x = –14 10x 14 ᎏᎏ = –ᎏᎏ 10 10 x = –ᎏ11ᎏ40 = –ᎏ75ᎏ = –1ᎏ52ᎏ Practice Be sure to write out your steps!
Checks and service charges are negative numbers. Balance your checkbook using positive and negative numbers. 19 Team-LRN Team-LRN L E S S O N 2 Working with Algebraic Expressions LESSON SUMMARY In this lesson, you will use the same rules of signs that you learned in the previous lesson for any number—including fractions—not just integers. You will find out how to simplify and evaluate expressions and see how using the order of operations can help you find the correct answer. Simplifying Expressions What does it mean when you are asked to simplify an expression?
Combine like terms. 2(x + y) + 3(x + 2y) 2x + 2y + 3x + 6y = 5x + 8y Tip If there is no number in front of a variable, it is understood to be 1. Here are two more examples using the distributive property. Example: 2(x + y) + 3(x – y) Multiply 2 times x and 2 times y. Then multiply 3 times x and 3 times (–y). When you multiply 3 times (–y), this is the same as 3(–1y). The 1 is understood to be in front of the y even though you don’t see it. In this example, you can see how the parentheses are used to indicate multiplication.
Algebra success in 20 minutes a day by Barbara Jund