1. One -Step Inequalities
Today’s Lesson:
What:
One -Step Inequalities
Why:
To solve one –step inequalities.

2. In an equation, there is _________ and only ________answer!!!
warm-up-- Solve the below equations:
x = 9
2) x = -2
In an equation, there is _________ and only
________answer!!!
x = -6
x = -3
ONE
ONE

3. What is an inequality??
Examples: 1)
3x > 99 3
x > 33 2)
x – 4 ≤ 44
x ≤ 48
Meaning:
“x” is ALL #’s bigger than
33, but can ____________ be
33 itself!!
Meaning:
“x” is ALL #’s less than
OR ____________ to 48 !
NOT
EQUAL
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.
one
infinite

4. Solve the following one-step inequalities:
x + 6 ≥ -4
Meaning:
x - (-3) < -25
x ≥ -10
x < -28
“x” is ALL numbers bigger than OR EQUAL to -10 !
“x” is ALL numbers SMALLER than -28,
but can NOT be -28
Itself !!

5. 3) 𝑥 7 ≤ -5
Meaning:
4) x > 88
x ≤ -35
x > 11
“x” is ALL numbers SMALLER than OR EQUAL to -35!
“x” is ALL numbers GREATER than 11, but NOT 11 itself!

6. Is the coefficient negative?
What about when a negative # is “with” x?
Solve: x > 16
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
– 4x ≥ -24
x ≤ 42 NO
YES
YES NO

7. Switch sign because the coefficient is negative!!
Circle EVERY number that could be a
solution to the following inequalities
(switch sign when needed):
-8 + x ≥ -14
x ≥ -6 -6
-6.5 -7 6
Switch sign because the coefficient is negative!!
-3x < -30
x > 10 10 9
10.5 11 8

8. Switch sign because the understood coefficient is negative!!
3) x ≤ 4
Switch sign because the understood coefficient is negative!!
x ≥ 20 19
-19
-20 20 21
4) 𝑥 7 > -9
x > -63
-63
-61
-62.5
-64
-62

9. 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 (entitled “Practice Work”) represent the homework assigned for that day.

10. Math-7 NOTES warm-up-- Solve the below equations:
DATE: ______/_______/_______
What: “One -Step Inequalities”
Why: To solve one –step inequalities.
NAME:
warm-up-- Solve the below equations:
x + 15 = 9 2) 4x + 10 = -2
In an equation, there is __________ and only __________ answer!!!
What is an inequality??
Examples:
1) _3_ x > _99_ ) x – 4 ≤ 44
x > x ≤ 48
Meaning: Meaning:
“x” is all #’s bigger than 33, but “x” is all #’s less than OR ____________
can _______________ be 33 itself! 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 the following one-step inequalities:
x + 6 ≥ -4
Meaning: _____________________________________
________________________________________________
x - (-3) < -25

11. What about when a negative # is “with” x? Solve: -4x > 16 QUESTION: 7
Meaning: _____________________________________
________________________________________________
4) x > 88
What about when a negative # is “with” x?
Solve: x > 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)
2x < -16
x_ > -5 -4
– 4x ≥ -24
x ≤ 42
Circle EVERY number that could be a solution to the following inequalities
(switch sign when needed):
-8 + x ≥ -14
-3x < -30
x ≤ 4
4) x > -9 7 -6
-6.5 -7 6 10 9
10.5 11 8 19
-19
-20 20 21
-63
-63.5
-62.5
-64
-62

12. “solving one-step inequalities”
Name: _____________________________________________________________________________ Date: _____/_____/__________
Math-7 PRACTICE
“solving one-step inequalities”
Directions: Solve each inequality.
Directions: Circle EVERY number that could be a solution to the following inequalities:
𝒙 𝟑 > -2 -5 -6 -7
-6.5
-5.5
x > -6 3 4 2 -3
𝒙 −𝟒 < 5
-22
-21
-20
-19
-18