Vocabulary
Simplify & Solving with Rational Expressions
Proportions
Inequalities
Absolute Value Equations
100
The following example demonstrates this property of exponents: (5y9)3 = 125y27
What is the power of a product rule?
100
Simplify (81 - r2) / (r + 9)
What is -(r - 9) = -r + 9
100
Solve for x. (x+1) / (2x + 3) = 2 / 3
What is x = -3
100
3 < 6x - 8 < 14
What is 11/6 < x < 11/3
100
|3r| = 9
What is r = 3 or -3
200
h(x) = (5x2 + 9x - 16) / (7x - 16) x can be any real number except for 16/7. This restriction on x is called this.
What is the domain?
200
Simplify (3x2 - 5x - 2) / (6x3 + 2x2 + 3x + 1)
What is (x - 2) / (2x2 + 1)
200
Four times the reciprocal of a number equals 12 times the reciprocal of 48. That number is _____.
What is 16?
200
Write your answer in interval notation. 5x - 9 <= 26 or 12x - 7 > 32
What is (-infinity, 7] or (13/4, infinity)
200
|16t - 8100| = -2
What is no solution?
300
A rational expression is written in the form P / Q where P and Q are polynomials. This is the other restriction.
What is Q (the denominator) cannot be equal to zero.
300
Solve [(g + 5) / 4] + [(g + 5) / 2] = a/8
What is a = -6
300
A couple wants to paint their home. If Alex works alone, Alex can apply one coat of paint in 6 hours. If John works alone, John can apply one coat of paint in 5 hours. If Alex and John work together at the same rate, it takes this many hours to paint the entire house. Round to the nearest tenths place, if necessary.
What is 2.7 hours?
300
Write your response in interval notation. |x-9| - 8 > -6
What is (-infinity, 7) or (11, infinity)
300
|h/5 + 9| = 6
What is h = -15 or -75
400
One way to solve proportions is to use the following method as demonstrated here: 5/x = 15/45 --> 225 = 15x --> x = 15
What is cross products?
400
[q / (2q - 2)] + [(2q - 16) / (4q + 4)] = (2q - 3) / (q + 1)
What is no solution?
400
Marcus and Tony work at Concrete Surgeons. The manager is preparing an estimate for a customer. He knows that Marcus can prepare a slab of concrete by himself in 5 hours. The manager also knows that Tony can prepare the same sized slab in 3.5 hours. If labor costs are $45.50, the quote for labor should be this number if Marcus and Tony work together.
What is $93.68
400
| x/5 - 3 | - 8 >= -4
What is (-infinity, -5] or [ 35, infinity)
400
| (4x - 7) / 3| = |-14|
What is x = 49/4 or -35/4?
500
(450/3x) + 6 = 450/2x Given the following equation, you would multiply both sides of the equation by 6x, which is the ______.
What is the lowest common denominator (LCD)?
500
[5 / (a2+4a+3)] + [2 / (a2+a-6)] - [3 / (a2-a-2] = 0
What is a = 17/4
500
A boat can travel 12 miles upstream in the same amount of time it takes to travel 15 miles downstream. The current is 3 miles per hour. This number represents the speed of the boat in still water. Round to the nearest tenths place, if necessary.
What is 27 miles per hour?
500
| (x + 6) / 3 | >= 2
What is (-infinity, -12) or (0, infinity)
500
| x + 4 | = | 7 - x |
What is x = 3/2
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