Expressions & Properties
Write an algebraic expression for "5 more than a number n."
5 + n or n + 5
Solve: x + 5 = 12.
x = 7
Solve: 2x + 3 = 11.
x=4
Graph the solution to x > 3 on a number line. (Describe the graph.)
Open circle at 3, arrow right (values greater than 3).
In the equation d = 5t where d is distance and t is time, which is the independent variable?
t (time) is independent.
Simplify the expression: 3(2x + 4)
6x+12
Solve: 7x = 35
x = 5
Solve: 5y - 4 = 21.
y=5
Write an inequality for "a number t is less than or equal to 8."
t ≤ 8
Identify the dependent variable: A plant grows h centimeters after w weeks; h = 2w + 1.
h is dependent.
Use the distributive property to expand: 4(x - 3).
4x - 12
Solve: m - 9 = 16
m = 25
Solve: (1/2)z + 5 = 11.
z=12
Solve and graph: x - 5 < 2.
x < 7. Graph: open circle at 7, arrow left.
Make a table of ordered pairs for y = 3x when x = 0, 1, 2, 3.
(0,0), (1,3), (2,6), (3,9)
Combine like terms: 6a + 4 - 2a + 7.
4a + 11
Solve: -3p = 18.
p = -6
Solve: 4x/2 + 3 = 11. (First simplify then solve.)
x=4
Solve: 3n + 2 ≥ 11. Show the inequality solution set.
n ≥3. Graph: closed circle at 3, arrow right.
A taxi charges a $2 flat fee plus $1.50 per mile. Write an equation relating cost C (dependent) and miles m (independent). Then find the cost for 6 miles.
C = 2 + 1.5m; For m=6 → C = 2 + 9 = 11 dollars.
Translate to an expression: "The product of 7 and a number decreased by 9."
7n - 9
A number divided by 4 equals 6. Write and solve the equation.
x = 24
The sum of twice a number and 7 is 25. Write and solve the equation.
n=9
Describe in words the solution to -4 < x ≤ 2 and list three integers that satisfy it.
Integers: -3, -2, -1, 0, 1, 2. Description: values greater than -4 and up to and including 2.
Given the equation p = 4n - 3 where p is points scored after n rounds, explain how you would use a graph and table to analyze the relationship between n and p. (Describe what to look for and one thing the graph shows.)
Use table to list n and p values; graph points with n on x-axis and p on y-axis; analyze slope (4): each additional round adds 4 points; y-intercept -3 shows starting offset. The graph shows linear growth; check that table and graph match.