Inequalities
Solve:
- x + 5 > 6 and 1 + 2x ≤ - 5
x ≤ - 3
The quotient of a number and 3 is same as the difference of the number and 2. Find the number.
3
What is the slope of the line through (2, 3) and (6, 7)?
m = 1
If f(x) = 3x + 7, what is f(2)?
f(2) = 13
In which of the following inequalities must the inequality symbol be reversed in the solution?
A) - 2x > 7
B) x - 3 < 10
C) 2x > -15
A) - 2x > 7
Solve:
4x−3 ≤ 9 OR 2x+6 ≥ 18
x≤3 OR x≥6
A gallon of stain covers 200 square feet. How many gallons are needed to paint two coats of stain on a deck that measures 20 feet by 45 feet?
9 gallons
Find the equation of the line with slope 4 and y-intercept as - 3.
Write in standard form
y = 4x - 3
-4x + y = -3 or 4x - y = 3
Which of the following linear equations are functions?
A) y = 2x B) y = - 3x - 1
C) y = 8 D) x = 2
D is not a function
Note: All linear equations are functions except those of the form x = c which are vertical lines
When graphing inequalities, when is the closed dot/circle used?
Use a closed dot/circle for "≤" or "≥" symbols.
|2x - 6| = |10 - 2x|
x = 4
Thirty gallons of a 20% acid solution is needed for an experiment. Only 40% and 10% acid solutions are available. How much of each should be mixed to form the needed solution?
40% solution = 10 gallons
10% solution = 20 gallons
What is the slope-intercept form of a line passing through (0, 5) and (4, -3)?
y = -2x + 5
If a function f is evaluated at - 5, the value of the function is 12. Write this using function notation
f(- 5) = 12
How do you find the y-intercept of an equation?
To find the y-intercept, let x = 0 and solve for y.
- 15 + |2x - 7| ≤ - 6
- 1 ≤ x ≤ 8
The price of a small diamond ring was recently increased by 11%. If the ring originally cost $1900, find the mark-up and the new price of the ring.
Mark-up = $209
New Price = $2109
Write the equation of a line parallel to y=−2x+1 that passes through (1, 4)
y = - 2x + 6
If ____________ can be drawn so that it intersects a graph more than once, the graph is not the graph of a function
A Vertical Line
If you were to graph y = 2x and then y = 2x - 1 then
what would be the difference in the second graph?
It would be shifted down one unit from the graph of
y = 2x.
k + 7 > 2k + 2 ≥ -3k - 8
- 2 ≤ k < 5
Two jets depart from the same location and travel in opposite directions. One jet's speed is 480 mph and the other jet's speed is 510 mph. When will the jets be 1485 miles apart?
1.5 hours
Write the equation of a line perpendicular to the y-axis and passing through ( - 2 , - 3).
y = - 3
Find the domain of the function
g(x) = 1/x
If x = 0 then the function is undefined, hence x can be the set of all real numbers except 0
When solving an equation of the form |X| = a and a is positive, which is correct?
A) There is no solution
B) As a is positive, we solve only for X = a
C) |X|=a is equivalent to solving for X =a and X= - a
C) |X|=a is equivalent to solving for X =a and X= -a