advertisement

Name:________________________________________________________________________________Date:_____/_____/__________ Answer Bank: equal not one many Fill in the Blank: 1. An equation has only _____________ answer. It compares two quantities that are ________________. 2. An inequality has _________________ answers. It compares two quantities that are _______________ equal. Write an inequality for the following situations: 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. GRAPH… and then CIRCLE ALL of the choices that represent the following inequalities: 4. x < -4 -4 0 5 -10 -2 2 0 -3 5 Move the “x” to the left! Switch the sign! 5. 2 ≥ x 3 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 2) x – 4 ≤ 44 +4 +4 x ≤ 48 . . . BUT the MEANING is very DIFFERENT! Meaning: “x” is ALL #’s bigger than NOT be 33, but can ____________ 33 itself!! 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 Homework/ practice Due by next class! IXL: 7th Grade, U.4 & U.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 YES or NO > -5 YES or NO – 4x ≥ -24 x + -5 ≤ 42 YES or NO YES or NO Circle EVERY number that could be a solution to the following inequalities (switch the 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 IXL: 7th Grade, U.4 & U.5 Name: _____________________________________________________________________________ Date: _____/_____/__________ Math-7 INDIVIDUAL PRACTICE 6x > -48 - Re-write inequality, putting x on the left (switch sign). Remember to switch sign when you need to!