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Core Focus on Linear Equations

Learn how to simplify expressions and solve linear equations with the Distributive Property. Practice identifying terms, coefficients, and like terms. Quiz questions provided.

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Core Focus on Linear Equations

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  1. Lesson 1.3 Core Focus on Linear Equations The Distributive Property

  2. Quiz 1.2 State whether the equation is true or not with the given values. • 6x – 4y = 22 when x = 5 and y = 2 • x + 5 = y when x = 6 and y = 11 • y = – 3x – 1 when x = – 2 and y = – 7 TRUE FALSE FALSE

  3. Lesson 1.3 The Distributive Property Simplify expressions using the Distributive Property and combining like terms.

  4. Vocabulary 2x and 9 are each terms. Term A number or the product of a number and a variable. Constant Term that has no variable. Coefficient The number multiplied by a variable in a term. Distributive Property A property that can be used to rewrite an expression without parentheses. 2x + 9 9 is a constant. 2 is the coefficient of the term 2x

  5. Vocabulary Continued… Like Terms Terms that have the same variable raised to the same power. Equivalent Expressions Expressions that have the same value.

  6. The Distributive Property For any numbers a, b and c: a(b + c) = a ∙ b + a ∙ c a(b – c) = a ∙ b – a ∙ c

  7. Example 1 Use the Distributive Property to simplify each expression. a. 2(x + 6) = 2(x) + 2(6) = 2x + 12 b. c. –5(3x – 1) = –5(3x) – (–5)(1) = –15x + 5 Watch the signs when distributing a negative number.

  8. Extra Example 1 Use the Distributive Property to simplify each expression. a. 9(x + 4) b. −2(4x − 7) 9x + 36 −8x + 14

  9. Example 2 Find the product by using the Distributive Property and mental math. a. 4(103) b. 998  7 c. 8(6.5) 4(103) = 4(100 + 3) 4(100) + 4(3) 400 + 12 = 412 998  7 = 7(1000 – 2) 7(1000) – 7(2) 7000 – 14 = 6,986 8(6.5) = 8 (6 + 0.5) 8(6) + 8(0.5) 48 + 4 = 52

  10. Extra Example 2 Find the value of 8 ∙ 1002 using the Distributive Property and mental math. 8,016

  11. Example 3 A subtraction sign is treated as a negative sign on the coefficient it proceeds. Simplify by combining like terms. Mark terms that are alike. 3x – 2y + 4 – 2x + x + 4y Group like terms. 3x – 2x + x – 2y + 4y + 4 Combine like terms. 2x + 2y + 4

  12. Extra Example 3 Simplify by combining like terms. −4a + 5b + 3b − 2b + a −3a + 6b

  13. Example 4 Simplify by combining like terms: – 5(2x – 1) + 3x – 2 Distribute.– 5(2x – 1) + 3x – 2 = – 10x + 5 + 3x – 2 Group like terms.= –10x + 3x + 5 – 2 Combine. = – 7x + 3

  14. Extra Example 4 Simplify the expression. 2(3y − 5) + 8 − 6y −2

  15. Explore! Match Them Up Step 1 On your own paper, copy each expression below. Leave at least two lines between each expression. A. 2(x + 4) − 5 F. 20 − 3(x + 4) − 2x B. 3(x − 3) − 2x G. 3x + 3 + 7x − 8x C. 1 + 8(x + 1) H. −2(x − 3) + x + 5 D. 9 − 4x − 1 − x I. 2(x + 7) − 3(x + 1) E. 2(4x − 5) + 1 − 7x J. 6x + 5x − x − 2x + 9 Step 2 Simplify each expression. Step 3 Every expression listed above is equivalent to one other expression in the list. Classify the ten expressions into five groups of equivalent expressions. Step 4 Create another ‘non-simplified’ expression for each group that is equivalent to the other expressions in the group.

  16. Communication Prompt How could the Distributive Property help you do mental math in real-world situations?

  17. Exit Problems Simplify each expression. • 4(x − 3) • 9x + 2 + 3x – 4 − 7x • 10 + 8(2x + 3) − x 4x – 12 5x – 2 15x + 34

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