Name _____________________
Class & Block ______________
Date ______________________
Write an algebraic expression to represent each verbal expression.
1. ____________
seven more than the product of a number and 10
2. ____________
four less than the square of a number
3. ____________
the product of the cube of a number and -6
4. ____________
five times the sum of 9 and a number
5. ____________
twice the sum of a number and 8
6. ____________
the square of the quotient of a number and 4
7. ____________
the cube of the difference of a number and 7
Write a verbal expression to represent each equation.
8.
x – 5 = 12
9.
3a2 = a + 4
10.
b = 2(b + 1)
Write an inequality for each problem. Then solve. (Don’t graph)
11. ___________
Twenty less than a number is more than twice the same number.
12. ____________
Four times the sum of twice a number and -3 is less than 5.5 times that same number.
13. ____________
Nineteen more than a number is less than 42.
14. ____________
The difference of three times a number and 16 is at least 8.
15. ____________
One half of a number is more than 6 less than the same number.
16. ____________
Five less than the product of 6 and a number is no more than twice that same number.
Name _____________________
Class & Block ______________
Date ______________________
Write an absolute value inequality for each of the following. (Sketch a graph if needed.)
17. ____________
all numbers greater than or equal to 5 or less than or equal to -5
18. ____________
all numbers less than 7 and greater than -7
19. ____________
all numbers between -4 and 4
20. ____________
all numbers less than or equal -6 and greater than or equal to 6
Name the property illustrated in each statement.
21. 67 + 3 = 3 + 67
___________________
32. gx = xg
__________________
22. (2a + 3b) + 4c = 2a + (3b + 4c)
33. g(5*h) = (g*5)h
__________________
___________________
23. 4(a + 5b) = 4a + 20b
34. 6u + 12v = 6(u + 2v)
__________________
___________________
35. 8 * 1 = 8
__________________
24. (2 + 3)a + 7 = 5a + 7
36. 3 + (-3) = 0
___________________
25. k + 0 = k
___________________
__________________
37. x + y = y + x
__________________
26. 5 * (1/5) = 1
___________________
38. 8 + (3 + 9) = 8 + 12
27. If 3 + 5 = 6 + 2, then 6 + 2 = 3 + 5
__________________
___________________
39. 3 + 0 = 3
28. fh + 2g = hf + 2g
__________________
___________________
40. (3/x)(x/3) = 1
29. 5(m*n) = (5*m)n
__________________
___________________
41. (5x2 + x + 3)+15=(5x2 + x)+(3 + 15)
30. 1 * b2 = b2
____________________
31. 4(0) = 0
__________________
42. a + (-a) = 0
____________________
__________________
Name _____________________
Class & Block ______________
Date ______________________
43. If 7 * 2 = 14, then 14 = 7 * 2
45. If 2x = 3d and 3d = -4, then 2x = -4
____________________
44. If ab = 0, then a = 0 and/or b = 0
_____________________
46. m + (-8) = m + (-8)
___________________
_____________________
47. Explain the property demonstrated in each step:
a. 3c + 5(2 +c) = 3c + 5(2) + 5c
___________________
= 3c + 5c + 5(2)
___________________
= (3c + 5c) + 5(2)
___________________
= (3 + 5)c + 5(2)
___________________
= 8c + 10
___________________
48. Chemists use water to dilute acid. One important rule of chemistry is to always pour the acid
into the water. Pouring water into acid could produce spattering and burns.
a. Would you say that combining acid and water is commutative? __________________
b. Give an example from your life that is commutative. __________________________
c. Give an example from your life that is not commutative. ________________________
Name _____________________
Class & Block ______________
Date ______________________