7th Grade Math Pre-Algebra Unit 3 - Equations, Inequalities, Functions

Which equation below represents the following statement:

For the number k, three times the number is 450 less than eight times the number.
1. k = 450 - 8k
2. 3k = 8k - 450
3. 3k = 450 - 8k
4. 8k = 3k - 450
Check the correct solutions below:
1. 9 - 3b = 6b
  b = 3
2. 12x - 36 = - 5x + 32
  x = 4
3. 3m + 5.8 = 17.8 - 9m
  m = - 2
4. 4.5b - 7.2 = 3.2b + 8.4
  b = 12
What is the width of a rectangle whose perimeter, P, is 528 ft and whose width is m, and whose length is 3m + 12?

m = __________ ft
If an equation has no solution, then the solution set is the ______ set.
Solve the following equation:

1/2( - 48x + 50) = -4(3x - 7)

x = _______
Your boat's gas tank holds 100 gallons. The gas guage indicates that the tank is half-full. Which of the following inequalites shows the amounts of gas, G, you can put in the tank without overflowing.
1. G ≤ 100
2. G ≥ 50
3. G ≤ 50
4. G ≥ 100
Check the inequalities below that are true for the given value:
1. 24 ≤ 4b, b = 5
2. 16/x < 9, x = 2
3. 6m > 42, m = 7
4. b/4 > 3, b = 13
5. 6 ≤ x + 3, x ≥ 3
You are going to plant a garden with a fence around it. You have 200 ft of fencing. If the lenth of the garden is 4 times the width, what is the maximum width of the garden you can plant with the amount of fencing you have.

_____ ft
Check the correct solutions below:
1. 7 ≤ s/8 + 2
  s ≥ 40
2. 1/3(b + 5) > 1/4(b - 7)
  b > 41
3. 8 + 4(x - 3) < 2(x - 3)
  x < -1
4. -7/8 c ≤ 4
  c ≤ 4 4/7
Solve for n:

3/4 + 4n < 14 + 6n

n > ___
A special relation of ordered pairs (x,y) in which each member of the domain (x) is paired with exactly one member in the range (y) is called a _______.
Check the relations below that are functions:
1. { (15, 7) , ( -4, 6) , (7, 0), (-4, 8),
  ( -5, 2)}
2. Domain: -2, -1, 0 1, 3, 7
  Range: 3, -3, 5, 7 , 0
3. { ( 8.5, 6) , (8.4 , 7) , (8.3 , 8) , (8.1 , 8.5)}
4. A graph with the following data points:
  (0 , 1), (1 , -2), (1, -3), (1 , -4)
For the function y = 4x -7, which entry below is the range if the domain is { -3, -1, 0, 2.5, 8}
1. { 19, -11, -7, 25}
2. { 5, -11, -7, 25}
3. { -19, 11, -7, 3, 25}
4. { -19, -11, -7, 3, 25}
Which of the following is a linear equation in two variables?
1. y = 3x² - 7
2. 3ab = 2a + 5b
3. 4m - 25 = 2.9 - 0.5n
4. 4x + 7 = 3 - x + 2z
The graphs of all linear equations are _______ ________.
Solve the following linear equation for x = -6.5

5(y + 8.2) = -6.6 + 4(x - 3.2)

y = _____________
Which equation below represents the following set of ordered pairs;

{ ( -2, 13) , ( 0, 5) , (2, -3) , ( 7, - 23) }
1. y = x + 6
2. y = - 6x + 1
3. y = -4 x + 5
4. y = x + 14
Which of the following is the form "functional notation"?
1. y = 3x - 25
2. f(x) = 3x - 25
Which statement below is true:
1. In a function, x represents the range values and f(x) represents the domain valuies.
2. In a function, x represents the domain values and f(x) represents the range valuies.
3. Niether is true
The x-intercept of the graph of a linear equation is the x-coordinate where the graph crosses the x-axis. The y-coordinate of this point is ________.
What is the minium number of ordered pairs you need to graph a linear equation?
How many variables does a linear equation have if its graph is either a horizontal or vertical line?
What is the x-intercept of the graph of:

y = 6x - 24

x = ______
Britney goes to the store with $12 to buy cans of soda that cost $2 each. Write an equation for the amount of change (y) that Britney would receive for various numbers (x) of cans of soda she could buy. How many cans of soda can she buy and receive $0 in change?

________ cans
The slope is the same for any two points on a straight line.
1. Always true
2. Never true
3. Sometimes true
What is the slope of the line that passes through the following two points:

(5, 6), (8, 18)

slope = ______
What is the slop of the following equation:

4x - .8y = 7

slope = _________
Which of the equations below is the linear equation for the following two points:

(-4, 6) and (3, 2)
1. x = -4/7y + 26
2. y = 4/7 + 26
3. y = -4/7x + 26
4. y = -7/4 + 29
Your Dad goes on a diet. His weight (w) when he starts is 210 pounds. Every three days he loses 7.5 pounds. We write a linear equation that shows the relationship between his weight (w) and the number of days he is on the diet (d).

Which one below is the correct equation.
1. w = 210 - 7.5d
2. w = (-7.5/3)d +210
3. w = (7.5/3)d + 210
4. w = (-7.5)d - 210
At the start of school, you score 75 on a weekly quiz. In each of the following weeks you increase your score by 3 points. If you keep improving, what will you score be in the fifth week after your first quiz?
Which of the following are true?
1. The solution of a system of two linear eauations is the ordered pair that is a solution of both equations
2. If two linear equations have the same graph, there sre no solutions of this system of equations.
3. When you plot the graphs of two linear equations, the result is two parallel lines. This system of equations has no solution.
4. If the graphs of two linear equations intersect, then that system of equations has only one solution.
Solve for y:

x + 3y = 7
y = - 5x + 7

y = _________
Which system of equations represents the following verbal description?

The sum of two numbers is 14. The first number is 4 times greater than the second number.
If you plot the graph of the inequality:

x + y ≤ 25,

The boundary should be:
1. a dotted line since the boundary is not part of the graph.
2. a solid line since the boundary is part of the graph.
After you plot the graph of the related equation of an inequality, you determine that a point below the line is not a solution to the inequality. Which area should you shade to indicate thr region that contains all the points that are solutions to the inequality.
1. above the line
2. below the line