Solving Equations
Solving Inequalities
Vocabulary
Literal Equations
Word Problems
100
Solve for x
2x+4 = 8
2x+4 = 8
2x = 8 - 4
2x = 4
x = 2
100
Solve for x and graph the inequality
3x-5>7
3x-5>7
3x>12
x>4
100
A well-defined collection of distinct objects or elements. For example the image below is a ___ of geometric shapes
What is a set?
100
Solve for a
2a+3b=5c
2a+3b=5c
2a=5c-3b
a=(5c-3b)/2
100
A number decreased by 7 is greater than 12. Write and solve an inequality for the number.
x-7>12
200
Solve for x
4(x-2)+5=21
4(x-2)+5=21
4x-8+5=21
4x-3=21
4x=24
x=6
200
Write the inequality for this situation: "A number x is at most 12."
x<12
200
A number's distance from zero on the number line
What is absolute value?
200
Solve for t
d=rt+s
d=rt+s
d-s=rt
(d-s)/r=t
t=(d-s)/r
200
You have 5 times a number minus 3 equals 2 times the number plus 7. Find the number.
5x-3 = 2x+7
5x=2x+10
3x=10
x=10/3
300
Solve for x
4(1/2x+5)-10=2(x+5)
4(1/2x+5)-10=2(x+5)
2x+20-10=2x+10
2x+10=2x+10
10=10
Infinitely many solutions
300
Solve and graph:
− 2 ( 4 + x ) ≤ 10
−2(4+x)≤10
-8-2x≤10
-2x≤18
x≥-9
300
An equation with multiple variables.
What is a literal equation?
300
Solve for b
A=1/2bh
A=1/2bh
2A=bh
2A/h=b
b=2A/h
300
You have 50 dollars to spend on snacks. Each snack costs 2 dollars. Write and solve an inequality to find the highest number of snacks you can buy.
2x<=50
If solved:
x<=25
So you can buy up to 25 snacks
400
Solve for x
3 (2x-4)=8+6x-5
3 (2x-4)=8+6x-5
6x-12=8+6x-5
6x-12=6x+3
-12=3
No Solution
400
Solve and graph the compound inequality
2x+1>5 and 3x-4<11
2x+1>5 and 3x-4<11
2x>4 and 3x<15
x>2 and x<5
2<x<5
400
An equation that states a relationship among quantities.
For example:
1. The chemical ________ of water is H2O
2. a^2+b^2=c^2 is a _________ used to find the measures of the sides of right triangle
What is a formula?
400
Solve for r
V=pir^2h
V=pir^2h
V/h=pir^2
V/h*1/pi=r^2
V/(hpi)=r^2
sqrt(V/(hpi))=r
400
A car rental company charges a $40 flat fee plus $0.25 per mile. If your total bill was $70, write and solve an equation to find how many miles you drove.
0.25x+40=70
0.25x=30
x=120
500
Solve for x
(x+5)/2 = (3/2x-4)/6
(x-5)/2 = (3/2x-9)/6
3x-18=6x-30
3x+12=6x
12=3x
4=x
500
Solve and graph the compound inequality
2x+6 > 10 or -x+5 > 8
2x+6 > 10 or -x+5 > 8
2x>4 or -x>3
x>2 or x<-3
500
An algebraic equation that is true for all possible values of its variables
What is an identity?
500
Solve for h
A=(h(b1+b2))/2
A=(h(b1+b2))/2
2A=h(b1+b2)
2A/(b1+b2)=h
h=2A/(b1+b2)
500
Four friends Amy, Kate, Josh and Barry are driving to the Keys for Spring Break. As they plan their route,Amy takes note that any speed below 45 will waste the most fuel. Then, Barry adds that going past 70 mph would be just as wasteful because the car.
Part I. Which inequality best represents the case?
a) x<45 or x>70
b) x<=45 or x>=70
c) x<=40 or x>=70
d) x>=45 or x<=70
Part II. Which inequality represents the range of speed the car SHOULD maintain to be most efficient?
a) x>45 and x<70
b) x>=45 and x<=70
c) x<=45 or x>=70
d) x<50 or x>100
Part I A)
Part II B)