INEQUALITIES Targeted TEKS A 10 The student understands

INEQUALITIES Targeted TEKS: A. 10 The student understands there is more than one way to solve a Quadratic Equation and solves them using appropriate methods. (A) Solve Quadratic Equations using concrete models, tables, graphs, and algebraic methods

Equal or Unequal? • We call a math statement an EQUATION when both sides of the statement are equal to each other. – Example: 10 = 5 + 3 + 2 • We call a math statement an INEQUALITY when both sides of the statement are not equal to each other. – Example: 10 = 5 + 5

Inequality Signs • We don’t use the = sign if both sides of the statement are not equal, we use other signs. GREATER THAN (OR EQUAL TO) > LESS THAN (OR EQUAL TO) < <

DON’T FORGET THIS!!! • THE BIGGER SIDE OF THE SIGN IS ON THE SAME SIDE AS THE BIGGER # • THE SMALLER SIDE OF THE SIGN IS ON THE SAME SIDE AS THE SMALLER # – Examples: 10 < 15 or -4 > -12

Let’s Try Some! • 3 < 5 • 2 < < 7 • 22 > 10 • -65 • -10 < 4 • 32. 3 < 32. 5 -62

Our Friend, The Number Line • A number line is simply this… …a line with numbers on it. • We use a number line to count and to graphically show numbers. – Example: Graph x = 5.

Graphing Inequalities • Graph x = 2 • Graph x < 2 • Graph x > 2 A “closed” circle ( ) indicates we include the number. An “open” circle ( ) indicates we DO NOT include the number. By shading in the number line we are indicating that all the numbers in the shade are also possible answers.

You Try This… • Graph x < 10

You Try This… • Graph x > -4

You Try This… • Graph x > 200

You Try This… • Graph 7 < x

Let’s Go Shopping! • Last week you went shopping at the mall. You had $150 to spend for the day. You bought a shirt for $25 and some jeans for $40. You also spent $5 on lunch. You wanted to purchase a pair of shoes. What is the maximum amount of money you could have spent on the shoes? $150 > $25 + $40 + $5 + x The maximum amount you have The amount you have spent The cost of the shoes

How much can the shoes cost? $150 > $25 + $40 + $5 + x $150 > $70 + x -$ 70 -$70 $ 80 > x The cost of the shoes • Basically, the shoes must cost less than or equal to the amount you have left!

Do You Really Understand? • Let’s see if this makes sense… 3<9 (If we add 6 to both sides, is the inequality true? ) 3+6 < 9+6 9 < 15 YES!

Do You Really Understand? • Let’s see if this really makes sense… 10 > 4 (If we subtract 3 from both sides, is the inequality true? ) 10 -3 > 4 -3 7>1 YES!

Do You Really Understand? • Let’s see if this still really makes sense… 8 < 12 (If we multiply both sides by 2, is the inequality true? ) 8(2) < 12(2) 16 < 24 YES!

Do You Really Understand? • Let’s see if this still really makes sense… 8 < 12 (If we multiply both sides by -2, is the inequality true? ) 8(-2) < 12(-2) -16 < -24 -16 > -24 THIS STATEMENT IS NOT TRUE. WE NEED TO FLIP THE INEQUALITY SIGN TO MAKE THIS A TRUE STATEMENT.

Solving Inequalities • So apparently there a few basic rules we have to follow when solving inequalities. • If you break these rules you will answer the question incorrectly! • DON’T BREAK THE RULZ!

Rule #1 • Don’t forget who the bigger number is! – Example: 9>x – It is okay to rewrite this statement as x<9 – If 9 is bigger than “x”, that means that “x” is smaller than 9.

Rule #2 • When multiplying or dividing by a negative number, reverse the inequality sign. – Example: 15 > -5 x -5 -5 -3 < x

Solve Each Inequality & Graph Example 1: m + 14 < 4 -14 m < -10

Solve Each Inequality & Graph Example 2: 6 y - 6 > 7 y -6 y -6 > y y < -6

Solve Each Inequality & Graph Example 3: (-3) k < 10(-3) -3 k > -30