Linear Equations
Solve 2x+5=13
x=4
Solve: x-3>7
x>10
Simplify: x2⋅x3
x5
Is this a function and why or why not? {(1,2),(2,3),(3,4)}
Yes because each x (input) only has one y (output).
John has $10 and earns $5 per day. Write an expression for his total after x days.
y=5x+10
What is the slope of the line y=-3x+7
-3
On Desmos graph the inequality and identify one solution.
y≤ 2x+1
Answers may vary
Evaluate: (23)2
64
Identify the domain of the function f(x)=1/(x-3)
All real numbers except for 3.
A car rental costs $25/day plus $0.10 per mile. Write a function for total cost C
C(m)=0.10m+25
Write the equation of a line with slope 2 and y-intercept -4
y=2x-4
Solve the system:
y=2x+3
y=-x+6
(1,5)
Multiply: (x+2)(x-3)
x2-x-6
or
x2-1x-6
Given f(x)=2x+5, find f(3)
f(3)=11
A rectangle has a length of 2x and width of x+3. Write an expression for the area. Simplified
y=2x2+6x
Is the point (3,5) on the line y=2x-1? Justify your answer.
Yes
5=2(3)-1
5=6-1
5=5
Which values of x satisfy both x<5 and x≥-2?
-2≤ x<5
Simplify: 3x2+2x-x2+4x
2x2+6x
Compare the growth: Which grows faster, y=2x+3 or y=2x? Explain how you know.
y=2x
explanations may vary
You're buying pens for $2 each and notebooks for $3 each. You have $20. Write an inequality and provide one solution.
2x+3y≤ 20
Solutions may vary
Find the equation of the line that passes through (2,1) and (4,5).
y=2x-3
A ticket costs x dollars. You have $100 and want to buy at least 12 tickets. Write and solve an inequality to find the maximum cost per ticket.
12x≤ 100
x≤ 8.33
Max cost per ticket is $8.33
Factor: x2-5x+6
(x-3)(x-2)
or
(x-2)(x-3)
f(x)=3x-4
A phone plan charges $30/month and $0.05 per text. You want to spend at most $50. How many texts can you send?
30+0.05x≤ 50
-30 -30
0.05x≤ 20
/0.05 /0.05
x≤ 400, you can send up to 400 texts.