Operations on Real Numbers
Identify each solution as rational or irrational.
A. 4/7 + -1/3
B. Square root of 4 times 2/5
A. Rational
B. Rational
No. An irrational square root multiplied by itself will produce a rational result. An example: square root of 7 X square root of 7= square root of 49= 7.
Solve the equation. Check your solution.
4x + 2x - 5 = 25
x = 5
Classify the variable according to all the set of numbers that best describes its values.
The temperature t measured to the nearest degree Celsius.
Integers, Irrational Numbers, Natural Numbers, Rational Numbers.
Integers
Solve the equation.
7x + 2 = - 8 + 4x + 25
x = 5
Find the approximate side length of a square board with an area of 139 inches squared. Round to the nearest inch.
12 inches.
139 falls between the perfect squares 121 and 144.
Solve the equation. Check your solution.
5x + 3x - 5 = 43
x=6
Solve the equation.
5(4x + 7) = - 15 + 10
x = -2
In a volcano, erupting lava flows continuously through a tube system about 13 kilometers to the sea. Assume a lava flow speed of 0.5 kilometer per hour and calculate how long it takes to reach the sea.
13/ 0.5 = 26. It takes 26 hours to reach the sea.
Solve the following inequality.
x + 9 < 5
The solution is x < -4
Tell which set or sets the number below belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers.
Rational Numbers and Real Numbers
Solve the equation. Check the solution.
7 - 3x - 5 - 12x = 5
x= -1/5
Solve the equation without using the Distributive Property.
7.2(x - 2.75) = - 14.4
x = 0.75
Solve the equation.
2x + 1 = 2x + 1
The solution is all real numbers.
Solve the inequality and graph the solution.
x - 2 > - 7
x > - 5
Order the numbers below from least to greatest:
1/4, -4, square root of 2, -3/2, 4.9
-4, -3/2, 1/4, square root of 2, 4.9
Solve the equation.
5(2x + 7) = - 29 + 54
x = -1
Solve the equation.
6(3y - 1) - 3(2y) = 14
y = 10/6 or 5/3
6(x - 3) + 5 = 2x + 4( - 4 + x)
0 = -3; There is no solution.
Solve the equation.
3|d - 4| = 12
Is the difference of two rational numbers always a rational number? Explain.
Yes; the difference of two rational numbers can be rewritten as a single ratio, so the difference is always rational.
Solve the equation.
0.20x + 0.45(50) = 41.5
x = 95
Louie has a gift card for $45 that loses $2 for each 30-day period it is not used. He has another gift card for $35 that loses $1.50 for each 30-day period it is not used.
a. Write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal.
b. What will the value of each card be when they have equal value?
a. 45 - 2x = 35 - 1.50x; x = 20
b. When the gift cards have equal value, the value of each will be $5.
Solve the equation for the specified variable.
s = yh - 2yt^2
Solve for y.
y = s/ (h-2t^2)
Solve and graph each inequality.
|x + 3| < 10
-13 < x < 7