3.4 Solve Equations with Variables
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1 3.4 Solve Equations with Variables on Both Sides Goal p Solve equations with variables on both sides. Your Notes VOCABULARY Identity Example 1 Solve a 5 9a 2 5. Solve an equation with variables on both sides Collect variables on one side of the equation and constant terms on the other to solve equations with variables on both sides a 2 5 9a Subtract from each side Simplify Add to each side. 5 Simplify. 5 Divide each side by. 5 a Simplify. The solution is. CHECK ( ) 0 9( ) 2 5 Substitute for a Multiply. 5 3 checks. Copyright Holt McDougal. All rights reserved. Lesson 3.4 Algebra 1 Notetaking Guide 67
2 3.4 Solve Equations with Variables on Both Sides Goal p Solve equations with variables on both sides. Your Notes VOCABULARY Identity An equation that is true for all values of the variable Example 1 Solve a 5 9a 2 5. Solve an equation with variables on both sides Collect variables on one side of the equation and constant terms on the other to solve equations with variables on both sides a 2 4a 5 9a 2 4a 2 5 Subtract 4a from each side a 2 5 Simplify a Add 5 to each side a Simplify a Divide each side 5 by a Simplify. The solution is 4. CHECK ( 4 ) 0 9( 4 ) 2 5 Substitute 4 for a Multiply checks. Copyright Holt McDougal. All rights reserved. Lesson 3.4 Algebra 1 Notetaking Guide 67
3 Example 2 Solve an equation with grouping symbols Solve 4t (t 1 3). 4t (t 1 3) Write original 4t Distributive property Subtract from each side. 5 Subtract from each side. 5 t Divide each side by. Checkpoint Solve the Check your solution. 1. 3b b d } 3 (4d 1 8) 4 Example 3 Identify the number of solutions of an equation Solve the equation, if possible. a. 4x (x 1 5) b. 6x (2x 2 1) a. 4x (x 1 5) Original equation 4x Distributive property The equation 4x is because the number 4x equal to 5 more than itself and more than itself. So, the equation has solution. b. 6x (2x 2 1) Original equation 6x Distributive property The statement 6x is for all values of x. So, the equation is an. 68 Lesson 3.4 Algebra 1 Notetaking Guide Copyright Holt McDougal. All rights reserved.
4 Example 2 Solve an equation with grouping symbols Solve 4t (t 1 3). 4t (t 1 3) Write original 4t t 1 18 Distributive property t 1 18 Subtract 4t from each side t Subtract 18 from each side t Divide each side by 2. Checkpoint Solve the Check your solution. 1. 3b b d } 3 (4d 1 8) 4 b 5 1 d 5 4 Example 3 Identify the number of solutions of an equation Solve the equation, if possible. a. 4x (x 1 5) b. 6x (2x 2 1) a. 4x (x 1 5) Original equation 4x x 1 20 Distributive property The equation 4x x 1 20 is not true because the number 4x cannot be equal to 5 more than itself and 20 more than itself. So, the equation has no solution. b. 6x (2x 2 1) Original equation 6x x 2 3 Distributive property The statement 6x x 2 3 is true for all values of x. So, the equation is an identity. 68 Lesson 3.4 Algebra 1 Notetaking Guide Copyright Holt McDougal. All rights reserved.
5 Checkpoint Solve the equation, if possible. 3. } 1 (4t 2 6) 5 2t m (2 2 5m) Homework STEPS FOR SOLVING LINEAR EQUATIONS Step 1 Use the to remove any grouping symbols. Step 2 the expression on each side of the Step 3 Use the properties of equality to collect the terms on one side of the equation and the terms on the other side of the Step 4 Use the properties of equality to solve for the. Step 5 Check your in the original Copyright Holt McDougal. All rights reserved. Lesson 3.4 Algebra 1 Notetaking Guide 69
6 Checkpoint Solve the equation, if possible. 3. } 1 (4t 2 6) 5 2t 2 no solution 4. 10m (2 2 5m) identity Homework STEPS FOR SOLVING LINEAR EQUATIONS Step 1 Use the distributive property to remove any grouping symbols. Step 2 Simplify the expression on each side of the Step 3 Use the properties of equality to collect the variable terms on one side of the equation and the constant terms on the other side of the Step 4 Use the properties of equality to solve for the variable. Step 5 Check your solution in the original Copyright Holt McDougal. All rights reserved. Lesson 3.4 Algebra 1 Notetaking Guide 69
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