3.3 Solving Multi-Step Equations

3.3 Solving Multi-Step Equations

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  3.3 SOLVING MULTI-STEP EQUATIONS OBJECTIVE: TO USE TWO OR MORE TRANSFORMATIONS TO SOLVE AN EQUATION. MR. ANIBAL AGUILAR BARAHONA
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  3.3 SOLVING MULTI-STEPEQUATIONS As we explained in past sections, solving a linear equation may require two or more transformations. Use these guidelines in the process of solving an equation: • Simplify one or both sides of the equation (if needed). • Use the inverse operations to isolate the variable. The process of solving a linear equation may be presented in 4 general cases: CASE 1: Combining Like Terms. CASE 2: Using the Distributive Property. CASE 3: Distributing a Negative Sign. CASE 4: Multiplying by a Reciprocal
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  3.3 SOLVING MULTI-STEPEQUATIONS CASE 1: COMBINING LIKE TERMS. Solve the equation 2푥 − 9푥 + 17 = −4 Solution: 2푥 − 9푥 + 17 = −4 Copy the original equation −7푥 + 17 = −4 Combine the like terms. −7푥 + 17 − 17 = −4 − 17 Apply the inverse operation. −7푥 = −21 Combine like terms. 푥 = 3 Divide by -3 both sides.
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  3.3 SOLVING MULTI-STEPEQUATIONS CASE 2: USING THE DISTRIBUTIVE PROPERTY. Solve the equation: 4푥 + 12 푥 − 3 = 28 Solution: 4푥 + 12 푥 − 3 = 28 Copy the original equation. 4푥 + 12푥 − 36 = 28 Apply the Distributive Property. 16푥 − 36 = 28 Combine like terms. 16푥 − 36 + 36 = 28 + 36 Apply the inverse operation. 16푥 = 64 Combine like terms. 푥 = 4 Divide by 16 both sides.
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  3.3 SOLVING MULTI-STEPEQUATIONS CASE 3: DISTRIBUTING A NEGATIVE NUMBER. Solve the following equation: 10푥 − 6 2푥 + 5 = 20 Solution: 10푥 − 6 2푥 + 5 = 20 Copy the original equation. 10푥 − 12푥 − 30 = 20 Distribute -6 in the expression. −2푥 − 30 = 20 Combine like terms. −2푥 − 30 + 30 = 20 + 30 Apply the inverse operation. −2푥 = 50 Combine like terms. 푥 = −25 Divide by – 2 both sides.
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  3.3 SOLVING MULTI-STEPEQUATIONS CASE 4: MULTIPLYING BY A RECIPROCAL. Solve the equation: 4 3 푥 − 7 = −24 Solution: 4 3 푥 − 7 = −24 Copy the original equation. 3 4 4 3 푥 − 7 = −24 3 4 Multiply both sides by the reciprocal. . 푥 − 7 = −18 Simplify fractions on both sides. 푥 − 7 + 7 = −18 + 7 Apply the inverse operations. 푥 = −11 Simplify like terms.
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  HOMEWORK: PGS. 148– 149 EXERCISES 16 to 40