Real Numbers
To which subset does this number belong?
1.bar5
Rational Numbers
-4x+3(2x+5)=67
Solve
x=26
Solve for x
m=2x-2
x=(m+2)/2
x=1/2m+1
Solve
-2(3x-1)<8
x>-1
Solve
abs(c+3)=15
c=12 or c=-18
Which elements of the set of positive, odd integers less than 150 belong both to the subset of multiples of 3 and to the subset of multiples of 7?
21, 63, 105, 147
Solve
15x-5(-2+3x)=-10
No Solution
Solve for a
am=n+p
a=(n+p)/m
Solve
2x-(3-x)>x+1
x>2
Solve
4abs(v-5)+2=18
v=9 or v=1
Tell which set or sets the number below belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers.
-27
Integers, Rational Numbers, and Real Numbers
Solve
(x+24)/2+3=5
x=-20
Solve for a
u=(ak)/b
a=(ub)/k
Solve
2(3b+7)-6b>12
All Real Numbers
Solve
abs(2t+2/3)<=4
-7/3<=t<=5/3
Decide whether the difference represents a rational number or an irrational number.
15/23-sqrt5/5
Irrational
Solve
5x+7=-3+3x+22
x=6
Solve for x
-3x+2c=-3
x=(2c+3)/3 or x=2/3 c+1
Solve
3(x+3)-2<4 or 1-x<=-1
x<-1 or x>=2
Russel wants to buy 3 identical gift cards. He wants to make sure his total cost is no more than $2 above or below $60. Write an absolute value inequality to represent his situation.
abs(3c-60)<=2
Is the quotient of a nonzero rational number and an irrational number always irrational? Explain.
Yes; the quotient of a nonzero rational number and an irrational number can be rewritten as a ratio with a rational number in the numerator and an irrational number in the denominator, so the quotient will always be irrational.
Find three consecutive odd integers whose sum is 135.
43, 45, 47
Solve for a
g=4ca-3ba
a=g/(4c-3b)
Solve
-36<3p-6<-15
-10<p<-3
A plant that manufactures metal plates has a quality control team to check that the plates are the right size. A rectangular plate advertised as 5 cm long must have a length within 0.25 cm of 5 cm. Write and solve an absolute value inequality to find the minimum and maximum length of the plates.
abs(x-5)<=0.25
Minimum: 4.75 cm
Maximum: 5.25 cm