solve linear equations chapter 1.3. equations and expressions
TRANSCRIPT
Solve Linear Equations
Chapter 1.3
Equations and Expressions
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Equations Are Statements
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Solving Equations
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Solving Equations
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Properties of Equality
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Properties of Equality
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Solving a Linear Equation
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Solving a Linear Equation
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Solving a Linear Equation
• In the process of solving an equation, we change the original equation to a different one
• But because of the properties of equality, we are assured that the new equations have the same solution as the original
• These new equations are called equivalent equations because they have the same solution
• Now let’s see how we can use the number properties to solve an equation
• As we have done up to now, we will justify our steps
Solving a Linear Equation
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Given
1. Property of equality
2. Assoc. Prop. Add.
3. Inv. Prop. Add.
4. Ident. Prop. Add.
5. Property of equality
6. Assoc. Prop. Mult.
7. Inv. Prop. Mult.
8. Ident. Prop. Add.
9. Ident. Prop. Add. & Mult.
Solving a Linear Equation
• As before, you need not show every step; you may use the method you learned in past years
• However, it will to your benefit later if, rather than thinking of “dividing both sides”, you think of “multiply both sides by the reciprocal”
• The following example will illustrate why this is better
Solving a Linear Equation
1.
2.
3.
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9.
Given
1. Property of equality
2. Assoc. Prop. Add.
3. Inv. Prop. Add.
4. Ident. Prop. Add.
5. Property of equality
6. Assoc. Prop. Mult.
7. Inv. Prop. Mult.
8. Ident. Prop. Add.
9. Ident. Prop. Add. & Mult.
Variations
• In the next few examples I will use the same step-by-step method, but you need not do this on your howework
• However, you may be asked to name steps on a quiz or test!
• We will next look at variations of linear equations: with variables on both sides of the equation; with variables in parentheses
• But first, work the following example problems in your notes
Guided Practice
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Guided Practice
Guided Practice
Guided Practice
Variables on Both Sides of the Equal Sign
• Remember that part of our goal in solving an equation is to reach the form
• If an equation has variable terms on each side of the equal sign, we will need to collect variable terms on one side
• We can do this because, as you saw in the previous section, variable terms can be added/subtracted if they are like terms
Variables on Both Sides of the Equal Sign
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Variables in Parentheses
• Some equations may have variables within parentheses
• If the parentheses are multiplied by something, then we must use the distributive property to remove the parentheses
• If nothing multiplies the parentheses, they are unneeded and may be dropped
• Once parentheses are removed, it may be necessary to combine like terms on one or both sides of the equal sign
• Remember! You cannot combine like terms that are on opposite sides of the parentheses
Variables in Parentheses
Solve
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Guided Practice
Solve each equation.
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Exercise 1.3
• Page 21, #3-18
• Page 21, #21-31, odds
• Page 22, #33-39, odds
• Page 22, #55-61, odds
• Total: 30 problems