Variables and Algebraic Expressions/Evaluating Algebraic Expressions
Evaluate x + 7 for each member of the domain {4, 7, 10, 12}
Answer: 11, 14, 17, 19
What is the first step you should take in order to simplify this expression?:
-5(x + 7) + 4(x - 1)
Distribute
Write an equation
Quotient of a number and 15 is 120:
n/15 = 120
What should I do first?:
-2(j - 1) + 3(j + 4) = 8
Distribute
0.3x+0.05=0.3
100
List the variables and constants in this expression:
6x² + 5x - 7
Variables: x
Constants: 6, 5, -7
Simplify: -6(x+7)
-6x-42
Solve:
Quotient of a number and 15 is 120
n/15 = 120
n = 1800
Simplify & Solve:
-2(j - 1) + 3(j + 4) = 8
j + 14 = 8
j = -6
A tow truck charges a service fee of $75 and an additional fee of $1.50 per mile. What distance was Jeffrey’s car towed if he received a bill for $93?
12 miles
Translate this sentence into an expression:
Seventeen less than twice a number
2n - 17
Simplify: ⅗(x + 2)
⅗x + 6/5
The sum of the angles of a triangle is 180°. Find the measure of the third angle if the sum of the other two angles is 115°
x + 115° = 180°
x = 65°
Simplify and solve:
6 - 2(p + 4) = 108
-2p - 2 = 108
p = -55
Solve: (2x+3)/4 + (x-1)/6 = (x+4)/3
Multiply by 12:
3(2x + 3) + 2(x - 1) = 4(x + 4)
4x = 9
x = 9/4
Volume of a rectangular prism (V = lwh) when the length is 6 inches, the height is twice its length, and its width is 4 inches.
V = 6 × 4 × 12 = 288 in3 or cu. in.
Simplify:
-5(x + 7) + 4(x - 1)
-x - 39
Solve:
(x - 5)/2 = 9
x - 5 = 18
x = 23
Simplify and solve: 82b - 9b + 7 = 73b + 19
7 = 19 (Contradiction) ⇒ No Solution
A baseball pitcher needs more than one pitch to be effective. Daren uses his changeup half as much as he uses his fastball, and to save his arm, he throws a slider a fourth as much as his fastball. In a 140-pitch game, how many sliders would he throw?
Sliders = 20
Circumference of a circle whose radius is 7 meters (Leave in terms of pi)
C = 14π ≈ 43.98 m
Simplify:
-6[8x + 3(x - 4)] = -6[11x - 12]
-66x + 72
Justify each step for
5(x - 7) + 17 = 32:
5x - 35 + 17 = 32
5x - 18 = 32
5x - 18 + 18 = 32 + 18
5x = 50
5x/5 = 50/5
x = 10
Distributive Property
Combine Like Terms
Addition Property of Equality
Simplify / Addition
Multiplication Property of Equality
Simplify / Solution
Find three numbers whose sum is 40 if the first number is four more than the product of six and the second number, and the third number is nine less than twice the second number.
Let 2nd number = x, 1st = 6x + 4, 3rd = 2x - 9
(6x + 4) + x + (2x - 9) = 40 ⇒ 9x = 45 ⇒ x = 5
Jesse has $5.12. She has 3 more nickels than she does quarters, and she has half as many dimes as quarters. She has the same amount of pennies as she does dimes. How many of each coin does she have?
14 quarters, 17 nickels, 7 dimes, 7 pennies