Name:________________________________________________________________________________Date:_____/_____/__________
Happy
New Year!
Solve the following 1-step equations:
1)
x –(-4) = -10
2)
-6x = 60
x
−4
3)
= -2
Solve the following 2-step equations:
4) 3x + 2 = 17
5) 11 = -9x – 7
6)
x
−5
– 5 = -15
Solve the following miscellaneous “fraction” 2-step equations:
7)
2
x
5
+ 2 = -4
8)
𝑥+2
=
−4
4
Today’s Lesson:
What:
Inequalities
Why:
To identify and graph inequalities.
What is an inequality??
An inequality is a math sentence that
describes two or more quantities that are
_______
NOT equal. In other words, the left and
right sides of the inequality are NOT
__________________
.
balanced
inequality symbols . . .
Real-life examples . . .
What does an
inequality have to do
with real life??
Consider the following signs:
If x represents speed . . .
1) Inequality for obeying the
speed limit:
x ≤ 55
_________________________________
2) Inequality for not obeying
the speed limit:
_________________________________
x > 55
Real-life examples . . .
48”
BE AT LEAST THIS TALL
If x represents height . . .
3) Inequality for being able to ride:
x ≥ 48
_____________________________
4) Inequality for not being able to ride:
x < 48
____________________________
Real-life examples . . .
If x represents age . . .
5) Inequality for eating free:
x ≤ 10
_____________________________
6) Inequality for not eating free:
x > 10
____________________________
What does it mean??
In an equation, the variable (x) represents
ONE number. Is this true in an inequality??
Consider the following inequalities . . .
1) x > 25
2)
Meaning:
Meaning:
x is ALL numbers
SMALLER OR EQUAL
to 6.
x is ALL numbers
BIGGER than 25.
3)
x < 10
x≤6
4) x ≥ 12
Meaning:
Meaning:
x is ALL numbers
SMALLER than 10.
x is ALL numbers
BIGGER OR EQUAL
to 12.
for the test. . .
Circle EVERY number that could be a
solution to the following inequalities :
1)
x ≥ -6
0
-6
2)
-6.5
-7
6
-3
-2
x < -3
0
-3.5
-5
graphing an inequality. . .
Open or Closed Circle??
When graphing the answer to an inequality on a
open
number line, we use an __________________
circle for
closed
> or < signs, and a ______________________
circle for
≥ or ≤ signs.
How can you remember that? Here’s a little
trick:
DOES THE BIRD GET THE WORM ?!?
If the bird “gets the worm,” his belly is full, so
closed ( )
we use a ____________________________
circle. If
the bird does NOT get the worm, his belly is
open ( )
empty, so we use an _________________________
circle.
Graph the following inequalities on the
given number lines:
1)
x ≥ -4
2)
x < -4
3)
x > -1
4)
x ≤ 2
What about when “x” is on the right
side of the inequality??
Consider the following:
4 >x
x <4
Use common sense: If 4 is greater than x, then x
must be LESS than 4 !
If your age is greater than your sister’s age, then
less
your sister’s age must be _____________
than your
age! Makes sense.
So, in order to reduce careless mistakes, we
should re-write the inequality, placing “x”
on the LEFT side. HOWEVER, remember to
also switch the sign!! Let’s practice . . .
Graph the following inequalities on the given
number lines (re-write first):
1) 5 ≥ x
x ≤5
2) 0 < x
3) 7 > x
x >0
x <7
Homework/ practice
Due by next class!
IXL: 7th Grade,
U.1 & U.3
END OF LESSON
The next slides are student copies of the notes for this
lesson. These notes were handed out in class and
filled-in as the lesson progressed.
NAME:______________________________________________________________________________ DATE: ______/_______/_______
Math-7 NOTES
What:
Inequalities
Why:
To identify and graph inequalities.
What is an inequality??
An inequality is a math sentence that describes two or more quantities that are _______
equal. In other words, the left and right sides of the inequality are NOT __________________ .
inequality symbols . . .
Real-life examples . . .
Consider the following signs:
If x represents speed . . .
1) Inequality for obeying the speed limit: ______________________
2) Inequality for not obeying the speed limit: _________________
If x represents height . . .
3) Inequality for being able to ride: _____________________________
4) Inequality for not being able to ride: ________________________
If x represents age . . .
5) Inequality for eating free: _____________________________________
6) Inequality for not eating free: ________________________________
What does it mean??
In an equation, the variable (x) represents ONE number. Is this true in an inequality??
Consider the following inequalities . . .
1) x > 25
Meaning:
2)
x≤6
Meaning:
3)
Meaning:
4)
x ≥ 12
Meaning:
x < 10
for the test. . .
Circle EVERY number that could be a solution to the following inequalities :
1)
x ≥ -6
0
-6
-6.5
2)
-7
6
x < -3
0
-3.5
-5
-3
graphing an inequality. . .
Open or Closed Circle??
When graphing the answer to an inequality on a number line, we use an
_________________________ circle for > or < signs, and a __________________________
circle for ≥ or ≤ signs.
How can you remember that? Here’s a little trick:
DOES THE BIRD GET THE WORM ?!?
If the bird “gets the worm,” his belly is full, so
we use a ____________________________ circle. If
the bird does NOT get the worm, his belly is
empty, so we use an _________________________
circle.
Graph the following inequalities on the given number lines:
1) x ≥ -4
-2
2)
x < -4
3)
x > -1
4)
x≤ 2
What about when “x” is on the right side of the inequality??
Consider the following:
4 >x
Use common sense: If 4 is greater than x, then x must be LESS than 4!
If your age is greater than your sister’s age, then your sister’s age must be _____________
than your age! Makes sense.
So, in order to reduce careless mistakes, we should re-write the inequality, placing “x”
on the LEFT side. HOWEVER, remember to also switch the sign!! Let’s practice . . .
Graph the following inequalities on the given number lines (re-write first):
1) 5 ≥ x
2) 0 < x
3)
7 > x
IXL: 7th Grade, U.1 & U.3
Name: _____________________________________________________________________________ Date: _____/_____/__________
Math-7 INDIVIDUAL PRACTICE
Directions: Write an inequality for the following real-life situations:
1.
In the U.S., one must be at least 18 years of
age in order to vote. If x represents age,
write an inequality for people who are
able to vote.
2.
Driving through old-town Leesburg, the
speed limit is 25 mph. If x represents
speed, write an inequality for those who
are NOT speeding.
3.
At Hershey Park, one must be at least 52
inches tall in order to ride the Fahrenheit
rollercoaster. If x represents height, write
an inequality for those people who are
allowed to ride.
4.
In order for a car’s air bags to be activated,
a passenger must weigh a minimum of 90
lbs. If x represents weight, write an
inequality for when the air bags will NOT
be activated.
5.
You are instructed to spend no more than
$50 at the mall. If x represents money,
write an inequality for how much money
you are allowed to spend.
6.
The cheapest entrée at a certain restaurant
is $12. If you buy 2 entrees, write an
inequality that represents the minimum
amount of money you spent (let x
represent money).
Directions: Circle EVERY number that could be a solution to the following inequalities (remember to
re-write the inequality if x appears on the right side):
7.
x > -6
-5
-6
-7
-6.5
-5.5
8.
x ≤ 13
12
0
13
14
13.5
9.
3 > x
1
3
3.5
0
4
10.
x ≥ -20
-20
-100
0
-5
5
11.
15 < x
10
15
20
14
14.5
12.
x ≤ -10
-9
0
-10.5
-1,000
-10
Name: _____________________________________________________________________________ Date: _____/_____/__________
INDIVIDUAL PRACTICE
Match each inequality with its graph:
Does the
bird get
the worm?