Operations on Real Numbers
To which subset of the real number system does the number 1.257896154895 belong?
Rational Numbers.
-2(v -2) = -3 - 2v
No Solution
The sum of three consecutive odd integers is 45. What are the three integers?
13, 15, and 17.
xm = np , for x
x = (np)/m
−20 = −4x − 6x
x = 2
Order from least to greatest.
sqrt(4/9), 1/4, 0.6
1/4, 0.6, sqrt(4/9)
-4(v + 3) = -12 - 4v
Infinitely Many Solutions/
All Real Numbers
A rectangle has perimeter 182 in. and length 52 in. What is the width?
39 in.
z = b + (m/a) , for a
a = m/(z - b)
x − 4 = −9 + x
No solution.
Set G is the set of positive integers divisible by 4 and Set F is the set of perfect squares. List the first 5 elements of set H, which contains numbers in G that are also elements of F.
4, 16, 36, 64, 100
-3(v + 4) = 2v - 37
1 solution
A movie club charges a one-time membership fee of $25. This allows members to purchase movies for $7 each. Another club does not charge a membership fee and sells movies for $12 each. How many movies must a member purchase for the total cost of the two clubs to be equal?
5 movies.
u = kx + yx , for x
x = u/(k + y)
12 = −4( −6x − 3)
x = 0
Which elements of the set of natural numbers are also irrational numbers?
None.
4(k - 8) = -32 + 4k
Infinitely many Solutions/
All Real Numbers
Olivia ate at the same restaurant four times. Each visit she ordered a salad andleft a $1.50 tip. She spent a total of $54. Find the cost c of each sala
4c + 4 ∙ 1.5 = 54;
c = $12
-3a - 3 = -2n + 3p, for a
a = -(3 - 2n +3p)/3
−(7 − 4x) = 9
x = 4
Describe the error the student makes.
Carmen says that the sum of 11.2 and 19 will be irrational because 11.2 is not a rational number.
11.2 can be written in the form 112/10 , so it is a rational number. The sum of two rational numbers is always rational.
-(3 - 6b) = 6b + 5
No Solution
Mike has coffee worth $4 per pound that he wishes to mix with 20 pounds of coffee worth $7 per pound to get a mixture that can be sold for $5 per pound. How many pounds of the cheaper coffee should he use?
40 pounds.
12am = 4, for a
a = 1/3m
−5(1 − 5x) + 5( −8x − 2) = −4x − 8x
x = -5