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

In an equation, there is _________ and only ________answer!!! warm-up-- Solve the below equations: x + 15 = 9 2) 4x + 10 = -2 In an equation, there is _________ and only ________answer!!! x = -6 x = -3 ONE ONE

What is an inequality?? Examples: 1) 3x > 99 3 x > 33 2) x – 4 ≤ 44 +4 +4 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

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 !!

3) 𝑥 7 ≤ -5 Meaning: 4) 8x > 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!

Is the coefficient negative? 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? 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 + -5 ≤ 42 NO YES YES NO

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

Switch sign because the understood coefficient is negative!! 3) 24 - 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

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.

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_ 2) x – 4 ≤ 44 3 3 +4 +4 x > 33 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

What about when a negative # is “with” x? Solve: -4x > 16 QUESTION: 7 Meaning: _____________________________________ ________________________________________________ 4) 8x > 88 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) 2x < -16 x_ > -5 -4 – 4x ≥ -24 x + -5 ≤ 42 Circle EVERY number that could be a solution to the following inequalities (switch sign when needed): -8 + x ≥ -14 -3x < -30 24 - 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

“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: 13. 𝒙 𝟑 > -2 -5 -6 -7 -6.5 -5.5 14. -2x > -6 3 4 2 -3 15. 𝒙 −𝟒 < 5 -22 -21 -20 -19 -18