PRE-ALGEBRA

Lesson 2-4 Warm-Up

PRE-ALGEBRA Variables and Equations (2-4) equation – a number sentence with an “equal” sign Examples: = 11 a numerical expression equal to a numerical expression x + 7 = 37 or 37 = x + 7 an algebraic expression equal to a numerical expression (or vice versa) a + (-3) = 2a + 5 an algebraic expression equal to an an algebraic expression true equation – an equation in which both sides equal one another Example: = 18 false equation – an equation in which both sides don’t equal one another Example: 6 ≠ open sentence – an equation with one or more variables Example: Write the equation “nine times the opposite of five is forty-five.” State whether the equation is true, false or an open sentence. Words  nine times the opposite of five is forty-five 9 x (-5) = 45 The equation is false, because 9 x (-5) = -45, and -45 ≠ 45 What is an “equation”? What is a “true equation”, “false equation”, and “open sentence”?

PRE-ALGEBRA State whether each equation is true, false, or an open sentence. Explain. a. 3(b – 8) = 12 c. –9 + 5 = – 4 b. 7 – (–6) = 1 open sentence, because there is a variable =/ false, because 13 1 true, because – 4 = – 4 Variables and Equations LESSON 2-4 Additional Examples

PRE-ALGEBRA Write an equation for Six times a number added to the number is the opposite of forty-two. State whether the equation is true, false, or an open sentence. Explain. The equation is an open sentence, because there is a variable. Equation 6x6x += x –42 six times the number Words 6x6x added to x is the opposite of forty-two –42 the number Variables and Equations LESSON 2-4 Additional Examples

PRE-ALGEBRA Variables and Equations (2-4) solution of an equation – the value of the variable (what the variable is equal to) to make the equation true To check the solution to an equation, substitute to see if the variable makes the equation true. Example: On a mule ride, a rider and his gear weighs 185 pounds (lb.) If the gear weighs 20 pounds, does the rider weigh 160 pounds? Words  weight of rider plus weight of gear is 185 pounds Define  Let w = weight of rider Equation  w + 20 = = 185  Substitute or replace 160 for “w” to check). 180 ≠ 185  Simplify. No, the rider cannot weigh 160 pounds. Example: Can you stack eight books that are 3 in. thick inside a box that is 18 in. tall? 8 x 3 = in. ≠ 18 in.  Add up 3 in. eight times. No, you cannot stack all of the books inside the box. What is a “solution to an equation”? How do you check the solution to an equation?

PRE-ALGEBRA Is 45 a solution of the equation x = 75? x = 75 No, 45 is not a solution of the equation Substitute 45 for x =/ Variables and Equations LESSON 2-4 Additional Examples

PRE-ALGEBRA A gift pack must hold 20 lb of food. Apples weigh 9 lb and cheese weighs 5 lb. Can the jar of jam that completes the package weigh 7 lb? j= 20 Equation 5+=j20 weight of cheese Words plus = weight of jam. is20 lb weight of jam 9 j weight of apples plus Let j = 20 Add Substitute 7 for the variable. No, the jar of jam cannot weigh 7 lb =/ Variables and Equations LESSON 2-4 Additional Examples

PRE-ALGEBRA 1.Is b + 3b – 1 = 15 true, false, or an open sentence? 2.Write an equation for A number added to seven times the number is the opposite of thirty-two. Is the equation true, false, or an open sentence? 3.Is 25 a solution of the equation 175 – x = 150? 4.Can you stack eight books that are each 3 in. thick inside a box that is 18 in. tall? yes open sentence 7x + x = –32; open sentence no Lesson Quiz Variables and Equations LESSON 2-4