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Published byHilary Robbins Modified over 5 years ago

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Expression or Equation? 3x + 7 4y – 10 = 54 5z + 32 = 47 6x + 2y (8x – 1) 2 + y 2x = 16

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Objectives: 1. To be able to recognize the difference between an expression and an equation. 2. To be able to solve one step equations using a physical model.

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Expression or Equation?

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Solving One-Step Equations

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Definitions Term: a number, variable or the product or quotient of a number and a variable. examples: 12 z 2w c 6

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Terms are separated by addition (+) or subtraction (-) signs. 3a – ¾b + 7x – 4z + 52 How many Terms do you see? 5

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Definitions Constant: a term that is a number. Coefficient: the number value in front of a variable in a term.

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3x – 6y + 18 = 0 What are the coefficients? What is the constant? 3, 6 18

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Solving One-Step Equations A one-step equation means you only have to perform 1 mathematical operation to solve it. You can add, subtract, multiply or divide to solve a one-step equation. The object is to have the variable by itself on one side of the equation.

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Solving One Step Equations involving adding and subtracting. x + 7 = -13 What do need to do to both sides of the equation to get the variable by itself? - 7 What happens to the left side of the equation? x = What happens to the right side of the equation? -20 What is the solution of the equation?

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Solving One Step Equations. What would the previous equation look like if we used physical models to express it? x + 7 = -13 x Remember: = 0 +

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Solving One Step Equations. What would the following equation look like if we used physical models to express it? -5 = y - 12 Remember: = 0 + y

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Solving One Step Equations. What would the following equation look like if we used physical models to express it? 14 = a - 9 Remember: = 0 + a

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Example 1: Solving an addition equation t + 7 = 21 To eliminate the 7 add its opposite to both sides of the equation. t + 7 = 21 t + 7 -7 = 21 - 7 t = 14 t + 0 = 21 - 7

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Example 2: Solving a subtraction equation x – 6 = 40 To eliminate the 6 add its opposite to both sides of the equation. x – 6 = 40 x – 6 + 6 = 40 + 6 x = 46

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Example 3: Solving a multiplication equation 8n = 32 To eliminate the 8 divide both sides of the equation by 8. Here we “undo” multiplication by doing the opposite – division. 8n = 32 8 8 n = 4

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Example 4: Solving a division equation To eliminate the 9 multiply both sides of the equation by 9. Here we “undo” division by doing the opposite – multiplication.

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What are Inequalities?

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Inequality Signs Sig n Definition > Greater Than < Less Than ≥ Greater Than or Equal to ≤ Less Than or Equal to ≠ Not Equal to

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Just remember We read inequalities just like we read books, from left to right. Lets see how we read the following: You need to remember which sign it is. –Just as which would Pacman rather eat? –The bigger number! > 62 6 is greater than 2

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What does an open dot mean? 4 5 6 7 8 3210 4 5 6 7 8 3210 3.9 3.5 3.99 The value 4 is not included The value 4 is included

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What does an open dot mean? Si SignDot < ≤ > ≥ Open dot Closed dot Open dot

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Inequalities Inequalities are similar to equations when solving. You can add, subtract, multiply or divide any amount to either side as long as you do it to both sides.

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Graphing 1-variable Inequalities Steps 1.Read the inequality and identify the sign. 2.Draw a number line using the number from the inequality as the central number. 3.Label numbers to either side of it. 4.Place the appropriate dot on the number line on the central number. 5.Draw an arrow in the appropriate direction. (choose a number from the number line and test it in the inequality)

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Example: Graph the inequality: x < 10 The point for 10 in not included, so The circle is open. X is less than 10 10 11 12 13 14 9876 Now pick a point other then 10 and test it -Lets try 11 so 11<10 is not true so the arrow goes the other way

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12 13 14 15 16 17 18 19 20 Solve x - 6 < 10 and graph the solution. The point 16 in not included. The circle is open. +6

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4 5 6 7 8 9 10 11 12 -8

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Which of the following is the graph of r < 1? -3 -2 -1 0 1 2 3 4 5 A B C

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2 3 4 5 6 7 8 9 10 Write an inequality for the graph. Closed dot means the number 4 is included. x 4

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-6 -5 -4 -3 -2 -1 0 1 2 BACK

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0 1 2 3 4 5 6 7 8 9 9

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-6 -5 -4 -3 -2 -1 0 1 2 -4

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4 5 6 7 8 9 10 11 12 (6)

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When you multiply or divide each side of an inequality by a negative integer, you must reverse the order symbol.

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Do you change the sign if you multiply or divide by a positive number while solving? NO!!!!

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Do you change the sign? No Yes BACK

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