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Solving Linear Equations

Solving Linear Equations. Tutorial 3d. A Solution Set. Consider the different meanings of the word solution . The solution to the mystery escaped him. The word solution here refers to an explanation. The town’s solution to its landfill problem is to encourage recycling.

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Solving Linear Equations

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  1. Solving Linear Equations Tutorial 3d

  2. A Solution Set • Consider the different meanings of the word solution. • The solution to the mystery escaped him. • The word solution here refers to an explanation. • The town’s solution to its landfill problem is to encourage recycling. • Solution here refers to a method of solving a problem. • A chemist mixes two solutions to obtain a 15% acid solution. • Solution here refers to a homogeneous molecular mixture

  3. These examples illustrate that a solution set may have one member, more than one member, or no members. Solution Set • In Mathematics we also have different kinds of solutions and, therefore, different kinds of solution sets. • Study the table below:

  4. Solving:Addition & Subtraction Equations • One way to solve an equation is to get the variable alone on one side of the equal sign. • You can do this by using inverse operations, which are operations that undo one another. • Addition and subtraction are inverse operations. • You can use subtraction to undo addition and addition to undo subtraction .

  5. Solving:Addition & Subtraction Equations Example #1: Solve the equation x + 4 = 7 • Think to yourself: What is being done to the variable (x)? • A 4 is being added to the variable (x). Subtraction undoes addition therefore you should subtract a 4 on the left to get x alone on one side. • However, whatever you do to one side of an equation you must also do to the other side. x + 4 = 7 -4 -4 x = 3 Always check your answers! x + 4 = 7; Does x = 3? 3 + 4 = 7 is true therefore x = 3!

  6. Solving:Addition & Subtraction Equations Example #2: Solve the equation x - 12 = 20 • Think to yourself: What is being done to the variable (x)? • A 12 is being subtracted from the variable (x). Addition undoes subtraction, therefore you should add a 12 on the left to get x alone on one side. • However, whatever you do to one side of an equation you must also do to the other side. x - 12 = 20 +12 +12 x = 32 Always check your answers! x - 12 = 20; Does x = 32? 32 - 12 = 20 is true therefore x = 32!

  7. Problem Solving: A veterinary assistant holds a dog and steps on a scale. The scale reads 193.7 lb. Alone, the assistant weighs 135 lb. To find the weight of the dog, solve the equation w + 135 = 193.7 • Think to yourself: What is being done to the variable (w)? • A 135 is being added to the variable (w). Subtraction undoes addition therefore you should subtract a 135 on the left to get w alone on one side. • However, whatever you do to one side of an equation you must also do to the other side. w + 135 = 193.7 -135 -135 w = 58.7 The dog weighs 58.7 lb. Always check your answers! w + 135 = 193.7; Does w = 58.7? 58.7 + 135 = 193.7 is true!

  8. Solving:Multiplication & Division Equations • Multiplication and division are inverse operations. • You can use division to undo multiplication and multiplication to undo division.

  9. Solving:Multiplication & Division Equations Example #1: Solve the equation 5x = 35 • Think to yourself: What is being done to the variable (x)? • A 5 is being multiplied to the variable (x). Division undoes multiplication, therefore you should divide a 5 to the left side to get x alone on that side. • However, whatever you do to one side of an equation you must also do to the other side. 7 1 5x = 35 5 5 1 1 x = 7 Always check your answers! 5x = 35; Does x = 7? 5•7 = 35 is true therefore x = 7 !

  10. Solving:Multiplication & Division Equations Example #2: Solve the equation • Think to yourself: What is being done to the variable (r)? • A 6 is being divided into the variable (r). Multiplication undoes division, therefore you should multiply a 6 to the left side to get r alone on that side. • However, whatever you do to one side of an equation you must also do to the other side. 1 6•• 6 1 r = 24 Always check your answers!

  11. Solving:Multiplication & Division Equations Example #2: Solve the equation • Think to yourself: What is being done to the variable (r)? • A 5/6 is being multiplied to the variable (r). Multiplying by the reciprocal will eliminate the fraction, therefore you should multiply a 6/5 to the left side to get r alone on that side. • However, whatever you do to one side of an equation you must also do to the other side. 1 1 18 1 1 1 r = 108 Always check your answers!

  12. The End Time to move on to the assignment or the next lesson

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