Inequalities Today’s Lesson: What: Why: . . . so I can identify and graph inequalities. How: . . . by taking accurate notes, participating in ALL practice activities, and completing IXL homework with a 70% or greater.

How are equations and inequalities different?

Why is it important to re-write inequalities with “x” on the left of the inequality sign?

What is an inequality?? balanced 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 __________________ . NOT balanced

inequality symbols . . .

What does an inequality have to do with real life?? Real-life examples . . . What does an inequality have to do with real life?? Consider the following sign: If x represents speed . . . Inequality for obeying the speed limit: Inequality for not obeying the speed limit: x ≤ 55 x > 55

Real-life examples . . . 48” x ≥ 48 x < 48 Consider the following sign: BE AT LEAST THIS TALL If x represents height . . . Inequality for being able to ride: Inequality for not being able to ride: x ≥ 48 x < 48

Real-life examples . . . x ≤ 10 x > 10 Consider the following sign: If x represents age . . . 5) Inequality for eating free: 6) Inequality for not eating free: x ≤ 10 x > 10

x is ALL numbers SMALLER x is ALL numbers BIGGER OR EQUAL to 12. 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: x is ALL numbers SMALLER OR EQUAL to 6. x is ALL numbers BIGGER than 25. 3) x < 10 Meaning: 4) x ≥ 12 Meaning: x is ALL numbers BIGGER OR EQUAL to 12. x is ALL numbers SMALLER than 10.

for the test. . . Circle EVERY number that could be a solution to the following inequalities : x ≥ -6 -6 -6.5 -7 6 x < -3 -3.5 -5 -3 -2

How can you remember that? Here’s a little trick: 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. open closed closed ( ) open ( )

Graph the following inequalities on the given number lines: x ≥ -4 2) x < -4

x > -1 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. x < 4 less

What about when “x” is on the right side of the inequality?? 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): 5 ≥ x x ≤ 5 x ≤ 5 0 < x x > 0 7 > x x < 7 We want “x” on the LEFT!!

Wrap it up/Summary: How are equations and inequalities different? Why is it helpful to re-write inequalities with the “x” on the left of the inequality sign? Equations: Balanced The “x” can only be represented by 1 number There is only 1 answer Inequalities: Not balanced The “x” can be represented by many numbers There are many answers Because our brains think “left-to-right,” it helps to understand the meaning of the inequality. It makes it easier to graph 

video challenge. . .

Homework/ practice Due by next class! IXL: 7th Grade, T.2 and T.3 Score of 70 or higher

END OF LESSON