Solving Equations and Inequalities
Solve for x:
3x + 8 – 2(1 – x) = 1
x=-1
Which equation matches the graph drawn?
**Mrs. Shaw will draw :)
y=-3x+1
Which relation is not a function? Explain how you know
A.(2, 9), (−1, −5), (1, 5), (5, 0), (12, 3)
B.(−3, 1), (6, 2), (8, 3), (6, 4), (3, 5)
C.(5, 1), (4, 2), (3, 3), (2, 4), (1, 5)
D.(7, 2), (5, 3), (3, 4), (1, 5), (−1, 6)
B, the input 6 has more than one output
Solve the system by graphing. Write the solution as an ordered pair.
y = –3x + 3
y = 1/2x – 4
(2, -3)
How does the graph of f(x) = |x| compare with the graph of g(x) = -6|x|? Think about all the factors!
Vertex is the same but the graph is skinnier.
Domain is the same but the range changes to (-infinity, 0]
Order from least to greatest
√11, √(32/3), 22/7, 3.3
22/7 √(32/3), 3.3 √11
Write the equation of the line y = (–11/3)x + 3 in standard form.
11x+3y=9
Given f(x) = –3x, write an equation for f(x) + 4.
f(x)=-3x+4
Use substitution to solve the system of equations
2x + 3y = 6
y = –2/3x + 4
No solution
Graph the function:
f(x) = -1/3 |x +2|-3
Mrs. Shaw will judge answers :)
The sum of three consecutive integers is 84. What are the three numbers?
**Set up an equation and solve for full points!
27, 28, 29
What is the equation of the line through (−2, −2) and (4, −5)?
y= 1/2x-1
Find f(-4)
f(x)=32/(-x)+3^3
f(-4)=35
Use elimination to solve the system of equations:
3x + 4y = –20
6x + 5y = –7
(8, -11)
Find the vertex and axis of symmetry of the graph. Does it open upward or downward? What are the domain and range?
f(x) = 1.5|x − 3|+4
vertex: (3, 4)
AOS: x=3
Upward
Domain is (-infinity, infinity)
Range is [4, infinity)
Solve the equation d = gh – f for h
h=(d+f)/g
Which equation is the slope-intercept form of the line that passes through (1, 2) and is parallel to the graph of y = (8/3)x?
y=(8/3)x-(2/3)
On Saturdays, Eve earns $14 per hour for yard work and an extra amount for dog walking. Use the following information to write a linear function f Eve can use to determine her pay.
1 hour, $26
2 hours, $40
3 hours, $54
4 hours, $68
5 hours, $82
a(n)=15+(n-1)4
a(12)=59
f(x)=14h+12
Graph the inequality: y < –3x – 2
Mrs. Shaw will judge answers :)
DOUBLE JEOPARDY!
3 2/3 + (-2.25) + 8 / (-3)^2
10 5/12
Solve for x:
2/5(4x − 3) − 2x = (4/5) − x
x=10/3
Line p passes through point (0, 8) and is perpendicular to the graph of y = (1/4)x + 2. What is the equation of the line?
y=-4x+8
A tie-dye kit with one T-shirt costs $15. Each additional T-shirt costs $4 more.Write the explicit formula (a(n)=a(1)+(n-1)d) to represent the situation.
Use the formula to determine how much you will pay for 12 additional shirts.
a(n)=15+(n-1)4
a(12)=59
The cost of 5 hats and 1 scarf is $47. The cost of 2 hats and 2 scarves is $40. Write and solve a system of equations to determine how much does one hat costs?
h=6.75
-2x+3, x<-1
1/4x, x>-1
Mrs. Shaw will judge graphs.