Vocabulary
Define, "equation" and provide an example.
A mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15.
Solve for b and check your answer.
15+b=23
Solve for n and check your answer: 2(n+5)=−2
n= -6
Seven more than a number is less than 18. Find the number. Write and solve an inequality.
x+7 < 18
x < 11
Solve and graph 9x ≥ 3
x ≥ 1/3
Define, "inequality" and give an example.
A relationship that makes a non-equal comparison between two numbers or other mathematical expressions. For example, 3x< 7+3.
Solve for x and check your answer.
14x = −56
Solve for x: 9x−7=−7
x=0
Sue has $33 left for a cab fare home. The cab fare is $3 per mile. What is the maximum number of miles she will be able to travel in the cab?
3x ≤ 33
x ≤ 11 miles
Solve and graph: 10 + x > 17
x > 7
What are the three methods we use when solving equations and inequalities.
Inverse Operations
Distributive Property
Combining Like Terms
Last Friday Trevon had $29. Over the weekend he received some money for cleaning the attic. He now has $41. How much money did he receive? Write an equation and solve for the variable.
29+x=41
x=$12
Jill sold half of her comic books and then bought sixteen more. She now has 36. With how many did she begin? Write an equation and solve for the variable.
x/2+16=36
x= 40 comic books
A pilot must log at least 1100 training hours to fly an aircraft. Jim logged 300 hours. How many more hours must he log to qualify? Write an inequality and solve for the variable.
300+x ≥ 1100
x ≥ 800 hours
Solve and graph: x/9 ≤ 1
x ≤ 9
The main goal when we solve equations and inequalities is to...
Isolate the variable
Lisa is cooking muffins. The recipe calls for 7 cups of sugar. She has already put in 2 cups. How many more cups does she need to put in? Write an equation and solve for the variable.
2+X=7
X=5 cups
Aliyah had some candy to give to her four children. She first took ten pieces for herself and then evenly divided the rest among her children. Each child received two pieces. With how many pieces did she start?
(x-10)/4=2
x=18 pieces
While training for a marathon, you consume at least 2200 calories a day. For one session of exercise, you consume 400 calories. How many calories do you consume for the rest of the day?
400+x ≥2200
x ≥ 1800 calories
Solve and graph: 7x – 3 > 18
x > 3
The "flippin' inequality rule". This means flipping the inequality sign after multiplying or dividing by a negative number. For example, when solving -2x>6, to get the x by itself, you have to divide by -2. Since you're dividing by a negative number, you also have to flip the inequality sign: -2x/-2< 6/-2
Simplify both sides of the inequality to get your solution: x<-3.
Jenny wants to buy an MP3 player that costs $30.98. How much change does she receive if she gives the cashier $40? Write an equation and solve for the variable.
40-x=30.98
x= $9.02
For a field trip 4 students rode in cars and the rest filled nine buses. How many students were in each bus if 472 students were on the trip?
9x+4= 472
x=52 students
In 5 years, Nicole will be old enough to vote in an election. The minimum age for voting is at least 18 years. What can you say about how old she is now?
x+5 ≥ 18
x ≥ 13 years old
Solve and graph: 2x + 6 ≥ 4x
x ≤ 3