How do you identify equivalent expressions?

For ExampleAre 4(5x + 2) and 4(5x) +4(2)

equivalent expressions?

In this lesson you will learn to identify equivalent expressions

by using substitution.

Let’s ReviewLet’s ReviewOrder of Operations

Parentheses, Exponents, Multiplication and Division, Addition and Subtraction

3 x 2 + 9 -36 + 9 -3

15 -312

Let’s ReviewA Common MistakeRemember the Order of Operations

Wrong

Correct

5 x 3 + 4

15 + 419

5 x 735

Let’s ReviewCore LessonSam 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 + 16

Let’s ReviewCore Lesson

14x + 614(2) + 6

8x + 6(x + 1)8(2) + 6(2 +

1)28 + 6 8(2) + 6(3)34 16 + 18

3434 = 34

14x + 6 = 8x + 6(x + 1)

Let’s ReviewCore Lesson

14x + 614(4) + 6

8x + 6(x + 1)8(4) + 6(4 +

1)56 + 6 8(4) + 6(5)62 32 + 30

6262 = 62

14x + 6 = 8x + 6(x + 1)

Let’s ReviewCore Lesson

Use substitution to determine if 4(5x + 2) is equivalent to 4(2x + 5)

4(5(3) + 2) 4(2(3) + 5)4(15+ 2) 4(6 + 5)

4(17) 4(11)68 44≠

4(5x + 2) and 4(2x + 5) are not equivalent.

In this lesson you have learned to determine if expressions are

equivalent by using substitution.

Let’s ReviewGuided Practice

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

Let’s ReviewExtension Activities

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.

Let’s ReviewExtension Activities

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

Let’s ReviewQuick Quiz

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.