Operations on Real Numbers
A well-defined collection of elements
What is a set
Solve this equation:
100 = 8(4t - 5)
t = 4.375
4x + 3 < -6
x < -2.25
Solve the absolute value equation:
3 = |x| + 1
x = 2; x = -2
Lily buys 5 yards of red fabric and 8 yards of yellow fabric. The red fabric costs $2 more per yard than the yellow fabric. She pays a total of $62. What would be the combined cost of 1 yard of red and 1 yard of yellow fabric?
$10
True or False: The difference of a rational number and an irrational number is always rational.
False, Irrational number
Solve this equation:
1.045s + 0.068 = 15.743
s=15
Solve this inequality and graph the solution:
2.4x - 9 < 1.8x + 6
x< 25
Solve the absolute value inequality:
|2x - 5| < 9
x > -2 and x < 7
-2 < x < 7
The sum of three consecutive odd integers is 105. What are the three numbers?
33, 35, 37
What subsets of real numbers does -48 belong?
real number, integer, & rational number
Solve this equation:
0.45(t+8) = 0.6(t-3)
t = 36
Solve this compound inequality and graph the solution:
1/2x - 5 > -3 or 2/3x + 4 < 3
x > 4 or x < -1.5
|x| + 4 = -9
No solution
Liam combines x pounds of herbal tea at $6 per pound with 10 pounds of regular tea at $4 per pound. He makes a mixture that averages $5.50 per pound. Write an equation to model the situation
6x + 10(4) = 5.50( x + 10)
6x + 40 = 5.50 (x + 10)
*Order the following from least to greatest...
0.36363636..., square of 15, square root of 17/3
square root of 17/3, 0.36363636..., square root of 15
*Solve the Literal Equation
x=3(y-b)/m; solve for y
y=mx/3 +b
Solve the compound inequality and graph the solution:
2x -3 < 7 and 5 - x < 8
x>-3 and x<5
Solve the absolute value equation:
5|x+3| + 8 = 6
No solution
*The area A of the rectangle shown is described with the inequality 100 < A < 1,000. Write and solve a compound inequality for x.
Length:4x
Width: 5
5 < x < 50
Q = {-12, -11,- 6, -4, 2, 15, 32}
Which numbers are part of Set Q and multiples of 3?
{-12, -6, 15}
5(5t + 1) = 25t - 7
No solutions
Solve the compound inequality:
-x + 1 > -2 or 6(2x - 3) > -6
all real numbers
Solve the absolute value inequality:
-2|2x + 4| + 10 > -6
-6 < x < 2
***Write the formula for the volume of a cone V=1/3pie(rsquared)(h) in terms of h. Find the height h of a cone with volume V=32(pie)cmcubed and radius r=4cm.
Formula: h = 3V/(pie)(rsquared)
Height: 6cm