How do you identify equivalent expressions?

1. How do you identify equivalent expressions? For Example Are 4(5x + 2) and 4(5x) +4(2) equivalent expressions?

2. In this lesson you will learn to identify equivalent expressions by using substitution.

3. Order of Operations Parentheses, Exponents, Multiplication and Division, Addition and Subtraction 3 x 2 + 9 -3 6 + 9 -3 15 -3 12

4. Remember the Order of Operations 5 x 3 + 4 Wrong 5 x 7 35 Correct 15 + 4 19

5. Sam calculated the area of the garden below to be 14x + 6. Derek calculated the area of the garden to be 8x + 6(x +1). How can Sam and Derek check to see if 14x + 6 and 8x + 6(x + 1) are equivalent? 8 x x + 1 6

6. 8x + 6(x + 1) 14x + 6 8(2) + 6(2 + 1) 14(2) + 6 28 + 6 8(2) + 6(3) 34 16 + 18 34 34 = 34 14x + 6 = 8x + 6(x + 1)

7. 14x + 6 8x + 6(x + 1) 8(4) + 6(4 + 1) 14(4) + 6 56 + 6 8(4) + 6(5) 62 32 + 30 62 62 = 62 14x + 6 = 8x + 6(x + 1)

8. Use substitution to determine if 4(5x + 2) is equivalent to 4(2x + 5) 4(5(3) + 2) 4(2(3) + 5) 4(6 + 5) 4(15+ 2) 4(11) 4(17) 44 68 ≠ 4(5x + 2) and 4(2x + 5) are not equivalent.

9. In this lesson you have learned to determine if expressions are equivalent by using substitution.

10. Use substitution to show that 5x + 3(x – 2) is equivalent to 8x -6

11. Emily wanted to know if 14x + 3 and 6x + 3 + 2x were equivalent expressions. She substituted 0 in for x and saw that both expressions simplified to 3. She concluded that both expressions were equivalent. Explain why Emily’s substitution led to her incorrectly concluding they 14x + 3 and 6x + 3 + 2x were equivalent expressions. Include work to show that the expressions are not equivalent.

12. Use substitution to determine if the following expressions are equivalent. • 8(x + y) and 2x + 8y + 6x • 2a + 5(b – a) and 5b – 3a • 2(x – y) and x + x – y – y • 3x² + 6x – 8 and 5x -7 + 2x²

13. Use substitution to show that 4x – 8 is the same as 2(2x – 4). Use substitution to show that 3x + 4 and (x + 1) + (2x + 3) are equivalent expressions.