Name:________________________________________________________________________________Date:_____/_____/__________
Short Answer:
1. Describe the difference between an equation and an inequality.
Write an inequality for the following situations:
2. You must be at least 16 years of age in order to get a driver’s
license. If x represents age, write an inequality for those who are
old enough to get a driver’s license.
3. The riding lawn mower will not start unless the person on the
seat weighs a minimum of 100 lbs. Write an inequality that
represents when the mower will NOT start.
Circle ALL of the choices that represent the following inequalities:
4.
x ≤ -10
-9
0
-8
-10
-10.5
5.
2>x
3
2
0
-3
5
Graph the following :
6. x < 9
7. -4 ≥ x
Today’s Lesson:
What:
One -Step Inequalities
Why:
To solve one –step inequalities.
Solve the below equations:
1)
x + 15 = 9
x = -6
2)
4x + 10 = -2
x = -3
ONE and only
In an equation, there is _________
ONE
________answer!!!
Solving an inequality is very similar to
solving an equation . . .
Examples:
1) 3x > 99
3
3
x > 33
Meaning:
“x” is ALL #’s bigger than
NOT be
33, but can ____________
33 itself!!
2)
x – 4 ≤ 44
+4 +4
x ≤ 48
Meaning:
“x” is ALL #’s less than
EQUAL to 48 !
OR ____________
one
So, in an EQUATION, there is only __________________
answer. However, in an INEQUALITY, there is an
infinite
___________________________________
amount of
answers– as long as the answer “fits” the criteria.
Solve and graph the following one-step
inequalities:
1)
x + 6 ≥ -4
x ≥ -10
2)
-2 > x - (-3)
x < -5
Re-write the
inequality–
putting x on
the left!
Solve and graph the following one-step
inequalities:
3)
𝑥
2
≤ -4
x ≤ -8
4)
25 < 5x
x > 5
Re-write the
inequality–
putting x on
the left!
What about when a negative # is “with” x?
-4x > 16
Solve:
QUESTION:
Does the above answer still “work” when you plug
it back into the original inequality?
No, it does not work!
Memorize this rule:
When multiplying or dividing by a negative
number, we switch the inequality sign!!!
Is the coefficient
negative?
For the following inequalities, do we switch the
sign?? (Yes or No)
2x < -16
x_ > -5
-4
NO
YES
– 4x ≥ -24
x + -5 ≤ 42
YES
NO
Circle EVERY number that could be a
solution to the following inequalities
(switch sign when needed):
1)
-8 + x ≥ -14
x ≥ -6
0
-6
2)
-6.5
-7
6
Switch sign
because the
coefficient is
negative!!
-3x < -30
x > 10
10
9
10.5
11
8
3)
24 - x ≤ 4
Switch sign
because the
understood
coefficient is
negative!!
x ≥ 20
19
-19
-20
20
21
-64
-62
𝑥
> -9
7
4)
x > -63
-63
-61
-62.5
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.
NOTE: The last slide(s) in any lesson slideshow
represent the homework assigned for that day.
NAME:
DATE: ______/_______/_______
Math-7 NOTES
What: solving one -Step Inequalities
Why:
To solve one –step inequalities.
Solve the below equations:
1)
x + 15 = 9
2)
4x + 10 = -2
In an equation, there is __________ and only __________ answer!!!
Solving an inequality is very similar to solving an equation . . .
Examples:
1) _3_x > _99_
3
3
x > 33
Meaning:
“x” is all #’s bigger than 33, but
can _______________ be 33 itself!
2)
x – 4 ≤ 44
+4 +4
x ≤ 48
We still have to
isolate the
variable, and we
still follow the
Golden Rule . . .
Meaning:
“x” is all #’s less than OR ____________
to 48 !
So, in an EQUATION, there is only ____________________ answer. However, in an
INEQUALITY, there is an ___________________________________ amount of answers– as long
as the answer “fits” the criteria.
Solve and graph the following one-step inequalities:
1)
x + 6 ≥ -4
2)
Re-write the
inequality– putting
x on the left!
-2 > x - (-3)
3)
_x_ ≤ -4
2
4)
25 < 5x
What about when a negative # is “with” x?
Solve:
-4x > 16
QUESTION:
Does the above answer still “work” when you plug it back into the original
inequality?
Memorize this rule:
For the following inequalities, do we switch the sign?? (Yes or No)
𝑥
−4
2x < -16
– 4x ≥ -24
> -5
x + -5 ≤ 42
Circle EVERY number that could be a solution to the following inequalities
(switch sign when needed):
1)
-8 + x ≥ -14
0
3)
-6
-6.5
2)
-7
19
-19
-20
10
6
24 - x ≤ 4
-3x < -30
21
10.5
𝑥
7
4)
20
9
-63
-63.5
11
8
-64
-62
> -9
-62.5
Name: _____________________________________________________________________________ Date: _____/_____/__________
Math-7 homework
6x > -48
-
Re-write
inequality,
putting x on the
left (switch sign).
Remember to
switch sign when
you need to!