University:
Bradley University
Course:
MTH 109 | College Algebra
Academic year:

2023
Views:

121

Pages:

10
Author:

Angelica Rose

Warm-Up ? Solving with Variables on Both Sides Lesson Question How can you solve equations with variables on both sides of the equals sign? Lesson Goals Solve equations with variables on both sides. Isolate the variable term on one side and the Use the properties of constant equality to solve. on the other. W 2K Words to Know Write the letter of the definition next to the matching word as you work through the lesson. You may use the glossary to help you. C properties of equality A. to separate from other substances; to place apart B variable B. a letter or symbol used to represent an unknown quantity D coefficient C. the rules that allow you to balance, manipulate, and solve equations A isolate D. the number value in a monomial 1 Warm-Up Solving with Variables on Both Sides Using Algebra Tiles to Solve an Equation Use algebra tiles to solve 4x = 3x − 3. x x x x x − − − = x x 1. Isolate the x-term on the left side of the equation. • Drag 3 blue rectangular x-tiles to the right side. This makes 3 zero pairs and leaves no x-tiles on the right side. • Drag 3 blue rectangular x-tiles to the left side to keep the equation balanced. This makes 3 zero pairs and leaves 1 orange positive x-tile on the left side. x = − − − 4x = 3x − 3 x= 2 −3 Instruction Solving with Variables on Both Sides Slide 2 Isolating the Variable PROCEDURE Steps for Solving Solve the equation. 2x − 7 = 4x 1. Use the addition or subtraction property of equality to isolate the variable term. 2x − 7 = 4x −2x –2x −7 = 2. Use the multiplication or division property of equality to solve for the variable −7 2x = 2 2 . x = Verifying a Solution Verify that x = −7 is the solution for the equation 2x − 7 = 4x. 2  −7  2  − 7 =  2 − −7  4  14 28 −7 = − 2 2 −7 = −14 −14 = −14 So, our solution is correct. 3 2x −7 2    −7 2 Instruction Solving with Variables on Both Sides Slide 4 Solving for a Variable with Decimals on Both Sides EXAMPLE Steps for Solving Solve the equation. 1. Isolate the variable term to one side of the equals sign. 5.3x = 4.1x + 5.76 5.3x = 4.1x + 5.76 −4.1x −4.1x 1.2x 2. Use the inverse operation to remove the coefficient. 1.2x = 5.76 = 1.2 x = x = x= 4 5.76 1.2 5.76 10 × 1.2 10 57.6 12 4.8 Instruction Solving with Variables on Both Sides Slide 6 A One-Variable Equation with Fractions Solve the equation. Steps for Solving 1. Use the addition or subtraction property of equality to isolate the variable term. 8− 3 1 x= x 4 2 3 1 x = x 4 2 3 3 + x + x 4 4 8− 2. Use the multiplication or division property of equality to solve for the variable. 8= 4 4 5 i8 = i x 5 5 4 32 5 5 5x 4 = x Instruction Solving with Variables on Both Sides Slide 10 Solving More than One Way Solve the equation. 3x + 4 = 5x + 9 Isolate the variable term on the right. 3x + 4 = −3x 4= 5x + 9 −3x 2x −9 −5 +9 −2x + 4=9 5 −2x = −5 2x = 2 2 x = 3x + 4 = 5x + 9 − 5x − 5x −4−4 −9 = 2x Isolate the variable term on the left. −2x 5 = −2 −2 −5 2 x = − 6 5 2 Instruction Solving with Variables on Both Sides Slide 12 Solving an Equation with Fractions Solve the riddle. 9 minus three-fourths of a number is the same as seven less than half the number. 9− 3 1 x= x−7 4 2 3 1 x= x−7 4 2 3 3 + x + x 4 4 9− 5x 4 9= +7 16 = 16 i 64 5 5 x 4 4 4 5 = i x 5 5 4 = x 7 −7 7 Instruction Solving with Variables on Both Sides Slide 12 Verifying a Solution Verify that x = 64 is the solution for the equation. 5 9− 3 1 x= x−7 4 2 3  64  9−   = 4 5  9− 45 5 48 5 = 1 2 3 3 − =− 5 5 8    5 32 −7 5 − 48 = 32 − 5 5 Therefore, our solution is correct. 64 35 5 −7 Summary ? Solving with Variables on Both Sides Lesson Question How can you solve equations with variables on both sides of the equals sign? Answer (Sample answer) First, isolate the variable term on one side and the constant on the other; second, use properties of equality to solve for the variable. 2 Review: Key Concepts Steps to Solve 1. Use the addition or subtraction properties of equality to isolate the variable term and the constant on opposite sides of the equation. 2. Use the multiplication or division property of equality to solve for the variable. 9 Summary Solving with Variables on Both Sides Use this space to write any questions or thoughts about this lesson. 10

Warm Up Solving with Variables on Both Sides Answer Key

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