Summary 171 Section 3.3 Multiplication and Division Properties of Equality c a c b a c b c w 2 w 2 11 b 21112 w 22 3a 3 18 3 a 6 4x 4 20 4 4 4 x 20 4 x 5 x 16 2a Section 3.4 Solving Equations with Multiple Steps Key Concepts Steps to Solve a Linear Equation in One Variable 1. Simplify both sides of the equation. • Clear parentheses if necessary. • Combine like terms if necessary. 2. Use the addition or subtraction property of equality to collect the variable terms on one side of the equation. 3. Use the addition or subtraction property of equality to collect the constant terms on the other side of the equation. 4. Use the multiplication or division property of equality to make the coefficient of the variable term equal to 1. 5. Check the answer in the original equation. Examples Example 1 Solve: 41x 32 6 = 2x Step 1 Step 2 Step 3 Step 4 The solution is 3. 4x 12 6 2x 4x 18 2x 4x 2x 18 2x 2x 6x 18 0 6x 18 18 0 18 6x 18 6x 6 x 3 Check: 41x 32 6 2x Step 5 413 32 6 2132 4102 6 6 6 6 ✓ True 18 6 Key Concepts The Multiplication and Division Properties of Equality Let a, b, and c represent algebraic expressions, where c 0. 1. The multiplication property of equality: If a b, then 2. The division property of equality: If a b, then To determine which property to use to solve an equation, first identify the operation on the variable.Then use the property of equality that reverses the operation. Examples Example 1 Solve. Multiply both sides by 2. The solution is 22. Example 2 Solve. 3a18 Divide both sides by 3. The solution is 6. Example 3 Solve. 4x 20 and 4 x 20 The solution is 5. The solution is 16.
miller_prealgebra_2e_ch1_3
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