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 )
2
= −2ab −9ac = 8x
21. Example 1
Simplify.
a. − 2(n − 5) b. .3( x + .7)
= −2n +10 = .3x +.21
c. -(2ab + 9ac) d. 2x(4 x + 7y )
2
= −2ab −9ac = 8x
22. Example 1
Simplify.
a. − 2(n − 5) b. .3( x + .7)
= −2n +10 = .3x +.21
c. -(2ab + 9ac) d. 2x(4 x + 7y )
2
= −2ab −9ac = 8 x +14 xy
29. Dividing Variable
Expressions
Divide each term in numerator by denominator
Rewrite as distribution
3− x 1 3− x 1
= g = 2 (3 − x) = 2 − 2 x
3 1
2 2 1
31. 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
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
= 2x + 1
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 = (10 y − 5)
1
2
= +
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 = (10 y − 5)
1
2
= +
3 3
= 2x + 1 = 5y − 5
2
35. Example 2
Simplify. Practice both methods of division to see
which one you prefer.
1.6 − .8 z 9x + 5y
c. d.
−8 7
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
1.6 .8 z
= −
−8 −8
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
= −.2 + .1z
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 = .1z − .2
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
= − = (9 x + 5 y )
1
7
−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
= − = (9 x + 5 y )
1
7
−8 −8
9 5
= −.2 + .1z = .1z − .2 = x+ y
7 7
41. Example 3
Evaluate when x = 2 and y = -4.
2
a. − 3( x + 1) b. − 4 6 − y
42. Example 3
Evaluate when x = 2 and y = -4.
2
a. − 3( x + 1) b. − 4 6 − y
2
= −3x − 3
43. Example 3
Evaluate when x = 2 and y = -4.
2
a. − 3( x + 1) b. − 4 6 − y
2
= −3x − 3
2
= −3(2) − 3
44. Example 3
Evaluate when x = 2 and y = -4.
2
a. − 3( x + 1) b. − 4 6 − y
2
= −3x − 3
2
= −3(2) − 3
= −3(4) − 3
45. Example 3
Evaluate when x = 2 and y = -4.
2
a. − 3( x + 1) b. − 4 6 − y
2
= −3x − 3
2
= −3(2) − 3
= −3(4) − 3
= −12 − 3
46. Example 3
Evaluate when x = 2 and y = -4.
2
a. − 3( x + 1) b. − 4 6 − y
2
= −3x − 3
2
= −3(2) − 3
= −3(4) − 3
= −12 − 3
= −15
47. Example 3
Evaluate when x = 2 and y = -4.
2
a. − 3( x + 1) b. − 4 6 − y
2
= −3x − 3 = −4 6 − (−4)
2
= −3(2) − 3
= −3(4) − 3
= −12 − 3
= −15
48. Example 3
Evaluate when x = 2 and y = -4.
2
a. − 3( x + 1) b. − 4 6 − y
2
= −3x − 3 = −4 6 − (−4)
2
= −3(2) − 3 = −4 6 + 4
= −3(4) − 3
= −12 − 3
= −15
49. Example 3
Evaluate when x = 2 and y = -4.
2
a. − 3( x + 1) b. − 4 6 − y
2
= −3x − 3 = −4 6 − (−4)
2
= −3(2) − 3 = −4 6 + 4
= −3(4) − 3 = −4 10
= −12 − 3
= −15
50. Example 3
Evaluate when x = 2 and y = -4.
2
a. − 3( x + 1) b. − 4 6 − y
2
= −3x − 3 = −4 6 − (−4)
2
= −3(2) − 3 = −4 6 + 4
= −3(4) − 3 = −4 10
= −12 − 3 = −4(10)
= −15
51. Example 3
Evaluate when x = 2 and y = -4.
2
a. − 3( x + 1) b. − 4 6 − y
2
= −3x − 3 = −4 6 − (−4)
2
= −3(2) − 3 = −4 6 + 4
= −3(4) − 3 = −4 10
= −12 − 3 = −4(10)
= −15 = −40
52. Example 3
Evaluate when x = 2 and y = -4.
y-x
c.
x-y
53. Example 3
Evaluate when x = 2 and y = -4.
y-x
c.
x-y
−4 − 2
=
2 − (−4)
54. Example 3
Evaluate when x = 2 and y = -4.
y-x
c.
x-y
−4 − 2 −6
= =
2 − (−4) 6
55. Example 3
Evaluate when x = 2 and y = -4.
y-x
c.
x-y
−4 − 2 −6 6
= = =
2 − (−4) 6 6
56. Example 3
Evaluate when x = 2 and y = -4.
y-x
c.
x-y
−4 − 2 −6 6
= = = =1
2 − (−4) 6 6