Order of Operations
3 x 4 - 5 x 1
7
Evaluate the expression when z = 6.
4z - 7
17
Use the distributive property to determine if the following expressions are equivalent.
14 (x + 2) = 14x + 8
No, they are not equivalent.
14 (x + 2) = 14x + 28
Write an equation to represent the situation:
What number do you multiply by 7 to get 56?
7n = 56
Explain what it means to solve an equation.
To solve an equation means to find the value of the variable that makes the equation a true statement.
36 - 20 ÷ 4 x 3
21
Write the following expression in WORDS:
5a + 12
12 more than 5 times a number.
Use the distributive property to determine if the following expressions are equivalent.
23 x 5 - 23 x 9 = 23(5 - 9)
Yes, the expressions are equivalent.
Write an equation to represent the situation:
What number do you divide by 4 to get 16?
n ÷ 4 = 16
.
{0, 1, 3, 4, 5, 6, 7, 8, 9, 12, 20}
Use substitution to determine which number in the given set is a solution of the equation.
4x - 10 = 14
x = 6
(4 + 2)2 x 2
72
Write an expression to represent the admission to a museum of $18 and the cost of special exhibits s at $9 each. Evaluate your expression when s = 2.
18 + 9s
$36
Use the distributive property to find an equivalent expression.
12 (4x + 11)
48x + 132
Crooked Creek is putting on a musical. There are 95 people who are going to attend. The teachers determined that they would like to bring in a total of $475 from ticket sales. If x represents the price per ticket, write an equation to represent this situation.
95x = 475
.
{1, 2, 5, 6, 12, 20}
Use this set of possible solutions to determine a solution to the equation.
y ÷ 4 - 2 = 1
y = 12
3 x 36 ÷ (30 ÷ 5 x 2)
9
Write an algebraic expression for the verbal expression:
6 less than a number divided by 5.
n ÷ 5 - 6
At a birthday party, a deejay costs $40.88 plus $21.50 per hour. The cost of a bounce house is $39.50 per hour. Use the distributive property to write an expression to find the cost of the bounce and the deejay for a 2-hour party.
2(21.50 + 39.50) + 40.88
Write an equation to represent the situation:
The perimeter of a rectangle is 400 feet. The width of the rectangle is 80 feet. What is the length of the rectangle?
160 + 2l = 400
or
2(80) + 2l = 400
.
{1, 2, 3, 4, 5, 6, 10}
Use this set of possible solutions to determine a solution to the equation.
x2 − 8x + 15 = 0
x = 5
(1 + 3)2 x 5 ÷ 20 + 11
15
A photographer charges $75 for a wedding and $60 per hour. Write an algebraic expression to represent the situation. Evaluate the expression for a photographer that took pictures for 3 hours.
75 + 60h
$255
The high school is ordering new volleyball uniforms. A uniform costs $13 for a shirt, $11 for pants, and $8 for socks. There is a $20 shipping fee for the uniform order. Write an expression using the distributive property that represents the total cost to order 12 uniforms.
12(13 + 11 + 8) + 20
Ross had twice as many video games than Kristen. Together they had 93 video games. How many did Kristen have?
x + 2x = 93
Mrs. Wahl is measuring the dimensions of her triangular lot. She knows that the lot is in the shape of an isosceles triangle (two sides are equal), and the perimeter can be calculated by adding the lengths of the three sides. She knows that the perimeter is 450 feet and that the side that is different in length from the other two is 100 feet. She wants to calculate the length of the other two sides.
a. Write an equation that Mrs. Wahl can use to find the length of the other two sides of her lot, where x represents the length of one side.
b. Mrs. Wahl is not sure if the length of the other two sides is 100 feet, 150 feet, 175 feet, or 200 feet. Use substitution to find the solution to your equation and the length of the sides of Mrs. Wahl's lot.
a. 2x + 100 = 450
b. 175 feet