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Our Lesson

Our Lesson. Solving Equations by Multiplication and Division. Warm up. Find the value of the variable in the following:. 1. 6 + g = 3 w = -3. 2. 89 +j = 96 j = 7

rachel-puckett
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Our Lesson

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  1. Our Lesson Solving Equations by Multiplication and Division

  2. Warm up Find the value of the variable in the following: 1. 6 + g = 3 w = -3 2. 89 +j = 96 j = 7 3. 50 – p = 15.60 p = -34.4 4. q +3/4 = 1/8 q = -5/8 5. m + 12 = 5 m = -7 Confidential

  3. Lets review what we have learned in the last lesson Steps for Solving Equations 1) Isolate the Variable term (numerical coefficient of 1) you wish to solve for 2)Substitute your answer into the original equation and check that it works Confidential

  4. Isolating the variable term Example: x + 3 = 15 1) Isolate term with the variable x 2) It is important that we subtract 3 from both sides of the equation, otherwise we will lose equality. We now have: Subtract 3 from both sides (x + 3) – 3 = 15 – 3 x = 2 Here we solved for x by isolating by using opposite operations Confidential

  5. Substitute Your Answer into the Original Equation Substitution is a process of replacing variables with numbers or expressions For example, a + 12 = b, and a = 9, find the value for b 9 + 12 = b 21 = b By substituting, we switch or exchange values, often replacing a variable with a numerical value We substitute to minimize the number of variables in an expression, or to actually evaluate the expression or equation Confidential

  6. Lets Get Started Solving Equations with multiplication and division If a variable has the numerical coefficient of 1thenan equation can besolved by addingthe same numberto each sideor by subtractingthe same number fromeach side If numerical coefficientof variable is less than/morethan 1 (but not 1) we cansolve by multiplying or dividing each sideby the same number Confidential

  7. Multiplication and Division Properties of Equality For any real numbers a, b, and c, if a = b, then = a b a = b · c · c c c Example: If m 4 = 6 then If -4n = 8 then -4n 8 -4 -4 . . m 4 4 = 4 6 = Confidential

  8. The Multiplication Property of Equality and The Inverse Operation of Division If a = b, then ac = bc where c = 0 If c = d, then c= d where e= 0 e e Multiplying both sides of an equation by the same nonzero number produces an equivalent equation Confidential

  9. Steps for Solving Equations by Multiplication and Division 1. Isolate the variable you wish to solve for 2.Substitute your answer into the original equation and check that it works Confidential

  10. Step 1 Step 1: Isolate the variable itself When the variable does not have a coefficient of one, we will need to isolate the variable itself When the variable we wish to isolate is either multiplied or divided by a numerical coefficient or other variables that are not equal to one, we need to use either multiplication or division to isolate the variable Confidential

  11. Example of step 1 3x = 72 To solve this problem we want to isolate the x variable Since x is multiplied by 3, we should use the inverse operation of multiplication to isolate x That means we want to divide by 3. To isolate x, we simply divide both sides of the equation by 3 Confidential

  12. 3x = 72 24 3x = 72 3 3 x = 24 Confidential

  13. Step 2 Substitute Your Answer into the Original Equation Substitution is a process of replacing variables with numbers or expressions By substituting, we switch or exchange values, often replacing a variable with a numerical value We often substitute to minimize the number of variables in an expression, or to actually evaluate the expression or equation Confidential

  14. Example of step 2 3x = 72 x = 24 3(24) = 72 72 = 72 Confidential

  15. Solving Equations To solve equations, we can use properties of equality For any real number a, Reflexive – 5 + y = – 5 + y a = a, For all real numbers a and b, If 3 = 5x – 6, then Symmetric 5x – 6 = 3 b = a If a = b, then If 2x + 1 = 7 and 7 = 5x – 8 For all real numbers a, b, and c. Transitive If a = b, and b = c, then then, 2x + 1 = 5x – 8 a = c If (4 + 5)m = 18 If a = b, then a may be replaced by b and b may be replaced by a. Substitution then 9m = 18 Confidential

  16. Your Turn • 6m = 36 m = 6 • w/6 = 31 w = 186 • y/10 = 8.4 y = 84 • 3/5 z = 24 z = 40 • 18d = 36 d = 2 Confidential

  17. Your Turn • 3a = 18 a = 6 • 2k = - 12 k = -6 • v/3 = 60 v = 180 • 36s = 12 s = 1/3 • 10f = 120 f = 12 Confidential

  18. 1. An elephant, going at a speed of about 5 miles per hour, can walk faster than human. Find the time it takes for the herd to cover 50 miles. Use the formula d = r t, where d represents the distance traveled, r represents the rate or average speed and t represents the time. 10 hours Confidential

  19. 2.Four tenths time a number is 16. Find the solution 4/10 n = 16 n= 16 x 10 4 n = 40 4 Confidential

  20. 3.The cougars that are found in the colder regions of North and South America are about 75 inches long. They are about 1.5 times longer than the cougars that are found in the tropical jungles of Central America. 1.5c = 75 c = 75 x 10 15 25 2 50 inches = 3 Confidential

  21. Lets review what we have learned in this lesson Steps for Solving Equations 1. Isolate the variable you wish to solve for 2. Substitute your answer into the original equation and check that it works Confidential

  22. Step 1 Isolate the variable itself If the variable does not have a coefficient of one, we will need to isolate the variable itself When the variable we wish to isolate is either multiplied or divided by a numerical coefficient or other variables that are not equal to one, we need to use either multiplication or division to isolate the variable Confidential

  23. The Multiplication Property of Equality and The Inverse Operation of Division If a = b, then ac = bc where c = 0 If c = d, then c/e = d/e where e = 0 Multiplying both sides of an equation by the same nonzero number produces an equivalent equation Confidential

  24. Step 2 Substitute Your Answer into the Original Equation Substitution is a process of replacing variables with numbers or expressions By substituting, we switch or exchange values, often replacing a variable with a numerical value We often substitute to minimize the number of variables in an expression, or to actually evaluate the expression or equation. Confidential

  25. Great Job Today! Remember to practice what you learned! Confidential

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