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Essential Question: How do you write
equations and inequalities?
Before we
start…
When you compare things, what
phrases do you use?
For example, if you were to compare
the number of boys in class to the
number of girls.
– Tell your partner.
What is the difference between an
equation and an inequality?
• An equation is a
mathematical sentence
formed by placing the
symbol = between two
expressions.
• An inequality is a
mathematical sentence
formed by placing one
of the symbols <, ≤, >,
or ≥ between two
expressions.
What is an open sentence?
An equation or
inequality that
contains an algebraic
expression.
4x  8
How do you write equations and
inequalities?
• Look for key words or phrases that indicate an
equation or inequality.
• Translate to numbers, variables, operations and
symbols.
Translating to Equations and
Inequalities
Symbol
Meaning
=
<
≤
>
≥
is equal to
is less than
is less than or equal to
is greater than
is greater than or equal to
Associated Words
is, is the same as
is fewer than
is at most, is no more than
is more than
is at least, is no less than
Sometimes two inequalities are combined.
Translate to equations or inequalities.
The difference of twice a number k and 8 is 12.
The product of 6 and a number n is at least 24.
Translate to equations or inequalities.
A number y is no less than 5 and no more than
13.
The quotient of a number p and 12 is at least 30.
Translate to equations or inequalities.
The sum of twice a number r and 3 is 11.
A number q is at least 5 and less than 17.
The sum of 12 and the quantity 8 times a number
k is equal to 48.
The product of 9 and the quantity 5 more than a
number t is less than 6.
What is a solution?
A number when substituted
for the variable in an open
sentence makes the
equation or inequality true.
Solution of the equation
or a solution of the
inequality
How do you check possible solutions?
Substitute the number in for the variable.
Simplify.
Check if it is true.
Check whether 3 is a solution of the equation or inequality.
a. 8  2 x  2
c. 2 z  5  12
b. 4 x  5  6
d. 5  3n  20
Check whether 5 is a solution of the equation or inequality.
a. 24  3d  9
c. 2 w  7  3
b. 3 x  4  18
d. 4  3 p  19
Check whether the given number is a solution
of the equation or inequality.
9  x  4; 5
b  5  15; 7
2n  3  21; 9
Using Mental Math
• Some equations are simple enough to solve
using mental math.
• Think of the equation as a question.
• Once you answer the question, check the
solution.
Mountain Hiking The last time you and 3 friends went
to a mountain bike park, you had a coupon for $10 off
and paid $17 for 4 tickets. What is the regular price of 4
tickets? If you pay the regular price this time and share
it equally, how much does each person pay?
Guitar Lessons Sarah enrolled in a guitar class. The
enrollment fee was $25. She paid a total of $70 for the
enrollment fee and 3 lessons. What is the cost of 3
lessons? How much did each lesson cost?
Charity Walk You are taking part in a charity walk,
and you have walked 12.5 miles so far. Your goal is to
walk 20 miles. How many more miles do you need to
walk to meet your goal?
Eco-Challenge Eco-Challenge Fiji was a competition
that included jungle trekking, ocean swimming,
mountain biking, and river kayaking. In 2002, the U.S.
team finished second about 6 hours after the winning
team from New Zealand. The U.S. team finished in
about 173 hours. What was the winning team’s time?
Basketball A basketball player scored 351 points last
year. If the player plays 18 games this year, will an
average of 20 points per game be enough to beat last
year’s total?
Selling Coffee Mugs Tyler would like to make no less
than $610 selling coffee mugs online. If he sells 28
mugs for $22 each, will he achieve his goal?
Gymnastics You need to practice a gymnastic routine
for at least 25 hours. You have already practiced 8.5
hours. If you practice for another 16.5 hours, will you
reach your goal?
Compact Discs You buy a storage rack that holds 40
CDs. You have 27 CDs. Write an inequality that
describes how many more CDs you can buy and still
have no more CDs than the rack can hold. You buy 15
CDs. Will they all still fit?
• How do you write equations and inequalities?
Ticket Out the Door
• Write an equation or inequality on a piece of paper
(put your name on it) and place it in the box on your
way out…
The product of 4 and a number w is at most
51.