2. Essential Questions
How are variable expressions simplified?
How are variable expressions evaluated?
Where you’ll see this:
Part-time job, weather, engineering, spreadsheets
4. Vocabulary
1. Property of the Opposite of a Sum: The negative
outside the parentheses makes everything inside
it opposite
2. Distributive Property:
5. Vocabulary
1. Property of the Opposite of a Sum: The negative
outside the parentheses makes everything inside
it opposite
2. Distributive Property: Multiply each term inside the
parentheses by the term outside
6. Example 1
Simplify.
a. − 2(n − 5) b. .3( x + .7)
c. -(2ab + 9ac) d. 2x(4 x + 7y )
7. Example 1
Simplify.
a. − 2(n − 5) b. .3( x + .7)
c. -(2ab + 9ac) d. 2x(4 x + 7y )
8. Example 1
Simplify.
a. − 2(n − 5) b. .3( x + .7)
−2n
c. -(2ab + 9ac) d. 2x(4 x + 7y )
9. Example 1
Simplify.
a. − 2(n − 5) b. .3( x + .7)
−2n
c. -(2ab + 9ac) d. 2x(4 x + 7y )
10. Example 1
Simplify.
a. − 2(n − 5) b. .3( x + .7)
−2n +10
c. -(2ab + 9ac) d. 2x(4 x + 7y )
11. Example 1
Simplify.
a. − 2(n − 5) b. .3( x + .7)
−2n +10
c. -(2ab + 9ac) d. 2x(4 x + 7y )
12. Example 1
Simplify.
a. − 2(n − 5) b. .3( x + .7)
−2n +10 .3x
c. -(2ab + 9ac) d. 2x(4 x + 7y )
13. Example 1
Simplify.
a. − 2(n − 5) b. .3( x + .7)
−2n +10 .3x
c. -(2ab + 9ac) d. 2x(4 x + 7y )
14. Example 1
Simplify.
a. − 2(n − 5) b. .3( x + .7)
−2n +10 .3x +.21
c. -(2ab + 9ac) d. 2x(4 x + 7y )
15. Example 1
Simplify.
a. − 2(n − 5) b. .3( x + .7)
−2n +10 .3x +.21
c. -(2ab + 9ac) d. 2x(4 x + 7y )
16. Example 1
Simplify.
a. − 2(n − 5) b. .3( x + .7)
−2n +10 .3x +.21
c. -(2ab + 9ac) d. 2x(4 x + 7y )
−2ab
17. Example 1
Simplify.
a. − 2(n − 5) b. .3( x + .7)
−2n +10 .3x +.21
c. -(2ab + 9ac) d. 2x(4 x + 7y )
−2ab
18. Example 1
Simplify.
a. − 2(n − 5) b. .3( x + .7)
−2n +10 .3x +.21
c. -(2ab + 9ac) d. 2x(4 x + 7y )
−2ab −9ac
19. Example 1
Simplify.
a. − 2(n − 5) b. .3( x + .7)
−2n +10 .3x +.21
c. -(2ab + 9ac) d. 2x(4 x + 7y )
−2ab −9ac
20. Example 1
Simplify.
a. − 2(n − 5) b. .3( x + .7)
−2n +10 .3x +.21
c. -(2ab + 9ac) d. 2x(4 x + 7y )
−2ab −9ac 8x 2
21. Example 1
Simplify.
a. − 2(n − 5) b. .3( x + .7)
−2n +10 .3x +.21
c. -(2ab + 9ac) d. 2x(4 x + 7y )
−2ab −9ac 8x 2
22. Example 1
Simplify.
a. − 2(n − 5) b. .3( x + .7)
−2n +10 .3x +.21
c. -(2ab + 9ac) d. 2x(4 x + 7y )
−2ab −9ac 8 x +14 xy
2
30. Dividing Variable
Expressions
Divide each term in numerator by denominator
Rewrite as distribution
3− x 1 3− x
i
1
2
(3 − x)
2 2 1
3
2
− x
1
2
− x+
1
2
3
2
32. Example 2
Simplify. Practice both methods of division to see
which one you prefer.
6x + 3 10 y − 5
a. b.
3 2
6x 3
+
3 3
33. Example 2
Simplify. Practice both methods of division to see
which one you prefer.
6x + 3 10 y − 5
a. b.
3 2
6x 3
+
3 3
2x + 1
34. Example 2
Simplify. Practice both methods of division to see
which one you prefer.
6x + 3 10 y − 5
a. b.
3 2
6x 3
+
1
2
(10 y − 5)
3 3
2x + 1
35. Example 2
Simplify. Practice both methods of division to see
which one you prefer.
6x + 3 10 y − 5
a. b.
3 2
6x 3
+
1
2
(10 y − 5)
3 3
2x + 1 5y − 5
2
36. Example 2
Simplify. Practice both methods of division to see
which one you prefer.
1.6 − .8 z 9x + 5y
c. d.
−8 7
37. Example 2
Simplify. Practice both methods of division to see
which one you prefer.
1.6 − .8 z 9x + 5y
c. d.
−8 7
1.6 .8 z
−
−8 −8
38. Example 2
Simplify. Practice both methods of division to see
which one you prefer.
1.6 − .8 z 9x + 5y
c. d.
−8 7
1.6 .8 z
−
−8 −8
−.2 + .1z
39. Example 2
Simplify. Practice both methods of division to see
which one you prefer.
1.6 − .8 z 9x + 5y
c. d.
−8 7
1.6 .8 z
−
−8 −8
−.2 + .1z
.1z − .2
40. Example 2
Simplify. Practice both methods of division to see
which one you prefer.
1.6 − .8 z 9x + 5y
c. d.
−8 7
1.6 .8 z
− 1
(9 x + 5 y )
−8 −8 7
−.2 + .1z
.1z − .2
41. Example 2
Simplify. Practice both methods of division to see
which one you prefer.
1.6 − .8 z 9x + 5y
c. d.
−8 7
1.6 .8 z
− 1
(9 x + 5 y )
−8 −8 7
−.2 + .1z
9
x+ y
5
.1z − .2 7 7
42. Example 3
Evaluate when x = 2 and y = -4.
a. − 3( x + 1)
2
b. − 4 6 − y
43. Example 3
Evaluate when x = 2 and y = -4.
a. − 3( x + 1)
2
b. − 4 6 − y
−3x − 3
2
44. Example 3
Evaluate when x = 2 and y = -4.
a. − 3( x + 1)
2
b. − 4 6 − y
−3x − 3
2
−3(2) − 3
2
45. Example 3
Evaluate when x = 2 and y = -4.
a. − 3( x + 1)
2
b. − 4 6 − y
−3x − 3
2
−3(2) − 3
2
−3(4) − 3
46. Example 3
Evaluate when x = 2 and y = -4.
a. − 3( x + 1)
2
b. − 4 6 − y
−3x − 3
2
−3(2) − 3
2
−3(4) − 3
−12 − 3
47. Example 3
Evaluate when x = 2 and y = -4.
a. − 3( x + 1)
2
b. − 4 6 − y
−3x − 3
2
−3(2) − 3
2
−3(4) − 3
−12 − 3
−15
48. Example 3
Evaluate when x = 2 and y = -4.
a. − 3( x + 1)
2
b. − 4 6 − y
−3x − 3
2
−4 6 − (−4)
−3(2) − 3
2
−3(4) − 3
−12 − 3
−15
49. Example 3
Evaluate when x = 2 and y = -4.
a. − 3( x + 1)
2
b. − 4 6 − y
−3x − 3
2
−4 6 − (−4)
−3(2) − 3
2
−4 6 + 4
−3(4) − 3
−12 − 3
−15
50. Example 3
Evaluate when x = 2 and y = -4.
a. − 3( x + 1)
2
b. − 4 6 − y
−3x − 3
2
−4 6 − (−4)
−3(2) − 3
2
−4 6 + 4
−3(4) − 3 −4 10
−12 − 3
−15
51. Example 3
Evaluate when x = 2 and y = -4.
a. − 3( x + 1)
2
b. − 4 6 − y
−3x − 3
2
−4 6 − (−4)
−3(2) − 3
2
−4 6 + 4
−3(4) − 3 −4 10
−12 − 3 −4(10)
−15
52. Example 3
Evaluate when x = 2 and y = -4.
a. − 3( x + 1)
2
b. − 4 6 − y
−3x − 3
2
−4 6 − (−4)
−3(2) − 3
2
−4 6 + 4
−3(4) − 3 −4 10
−12 − 3 −4(10)
−15 −40
53. Example 3
Evaluate when x = 2 and y = -4.
y-x
c.
x-y
54. Example 3
Evaluate when x = 2 and y = -4.
y-x
c.
x-y
−4 − 2
2 − (−4)
55. Example 3
Evaluate when x = 2 and y = -4.
y-x
c.
x-y
−4 − 2
2 − (−4)
−6
6
56. Example 3
Evaluate when x = 2 and y = -4.
y-x
c. 6
x-y
6
−4 − 2
2 − (−4)
−6
6
57. Example 3
Evaluate when x = 2 and y = -4.
y-x
c. 6
x-y
6
−4 − 2
2 − (−4) 1
−6
6
