Solving Equations
Inequalities
One, Two, None, or Infinite Solutions?
Absolute Value Equations and Inequalities
100
Solve:
6x+16-4(1-x)=2
x=-1
100
Solve for x:
x-2x+10<x
x>5
100
Does this have one, none, or infinite solutions?
6x - 1 = -1
One solution:
x=0
100
How many solutions does this have?
|x+5|=-10
No solutions.
200
Solve:
3x+1=5(x-3)
x=8
200
Write the following inequality:
x<3
200
Does this have one, none, or infinite solutions?
x+1>10 or 2x+1 < 7
Infinite! Can be either x<3 or x>9.
200
How many solutions does this have?
|x+5|+10=10
One solution: x=-5
300
The following formula gives the perimeter, P, of a rectangle with side lengths W and L. Solve the formula for W:
P=2W+2L
W=(P-2L)/2
300
x>=-4 and x<=-1
-4<=x<=-1
300
Does this have one, none, or infinite solutions?
4x + 2x = 4(x-2) + 2x + 8
Infinite solutions
300
Solve:
2|x+4|+1=13
x=2 or x=-10
400
Gym Giant has a sign up fee of $35. Fitness World has a sign up fee of $95. Both also charge a monthly rate. An equation modeling the number of months, m, for which the two gyms cost the same is given below:
35+30m=95+10m
Which statement is true?
a) Gym Giant charges a lower monthly fee than Fitness World.
b) Fitness World charges $95 per month.
c) Gym Giant costs less to get started, but has a higher monthly fee.
d) After one month, a member of Gym Giant will have paid more than $100 total.
c) Gym Giant costs less to get started, but has a higher monthly fee.
400
Under his cell phone plan, Arturo pays a flat cost of $85.25 per month and $5 per gigabyte. Diane's cell phone plan charges no flat monthly fee but does charge $12.75 per gigabyte. Write and solve an inequality for g, the number of gigabytes when Arturo's plan costs more?
85.25 + 5g > 12.75g
g<11
400
Does this have one, none, or infinite solutions?
4x + 8 < 4x -10
None (no solutions)
400
Solve and graph:
|x+4|<=5
-9<=x<=1
500
A balloon is let go from the top of a 50 foot tall tree and is rising 5 feet per second. A peregrine falcon that absolutely hates balloons starts diving from an altitude of 2,930 feet traveling 355 feet per second intending to pop the balloon with its beak.
How long will it take the falcon to pop the balloon?
50+5s=2930-355s
s=8 seconds.
500
Solve and graph:
-5<=-2x-1<9
-5<x<=2
500
Does this have one, none, or infinite solutions?
2x<=-6 and -2x<-20
None (no solutions)
500
Solve and graph:
|2x-4|>10
x<-3 or x>7