How do you identify
equivalent expressions?
For Example
Are 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
Review
Let’s
Review
Order of Operations
Parentheses, Exponents, Multiplication and
Division, Addition and Subtraction
3 x 2 + 9 -3
6 + 9 -3
15 -3
12
A Common
Let’s
Review Mistake
Remember the Order of Operations
5x3+4
Wrong
5x7
35
Correct
15 + 4
19
CoreReview
Lesson
Let’s
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
CoreReview
Lesson
Let’s
14x + 6
8x + 6(x + 1)
14(2) + 6
8(2) + 6(2 + 1)
28 + 6
8(2) + 6(3)
34
34 = 34
14x + 6 = 8x + 6(x + 1)
16 + 18
34
CoreReview
Lesson
Let’s
14x + 6
14(4) + 6
8x + 6(x + 1)
8(4) + 6(4 + 1)
56 + 6
8(4) + 6(5)
62
62 = 62
14x + 6 = 8x + 6(x + 1)
32 + 30
62
CoreReview
Lesson
Let’s
Use substitution to determine if 4(5x + 2) is
equivalent to 4(2x + 5)
4(5(3) + 2)
4(15+ 2)
4(2(3) + 5)
4(6 + 5)
4(11)
4(17)
44
68
≠
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.
Guided
Practice
Let’s
Review
Use substitution to show that
5x + 3(x – 2) is equivalent to 8x -6
Extension
Let’s
ReviewActivities
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.
Extension
Let’s
ReviewActivities
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
Quick Quiz
Let’s
Review
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.