Glencoe Algebra 1 Chapter 4 Answer Key provides students with comprehensive solutions to the chapter’s practice problems, offering a valuable resource for understanding key concepts and mastering problem-solving techniques.
This chapter covers a wide range of topics, including solving equations with variables on both sides, solving inequalities with variables on both sides, solving absolute value equations and inequalities, and applications of equations and inequalities in real-world scenarios. With clear explanations and step-by-step solutions, the answer key helps students reinforce their understanding of these concepts and develop their problem-solving skills.
Glencoe Algebra 1 Chapter 4 Overview
Chapter 4 of Glencoe Algebra 1 introduces students to the concepts of solving equations and inequalities with variables on both sides, as well as absolute value equations and inequalities. The chapter also covers applications of equations and inequalities in real-world situations.
Learning Objectives:
- Solve equations with variables on both sides.
- Solve inequalities with variables on both sides.
- Solve absolute value equations and inequalities.
- Apply equations and inequalities to solve problems in real-world situations.
Solving Equations with Variables on Both Sides
An equation with variables on both sides is an equation in which the variable appears on both the left-hand side and the right-hand side of the equation. To solve an equation with variables on both sides, we need to isolate the variable on one side of the equation.
Steps for Solving Equations with Variables on Both Sides:
- Simplify both sides of the equation.
- Add or subtract the same number from both sides of the equation.
- Multiply or divide both sides of the equation by the same number.
- Continue simplifying until the variable is isolated on one side of the equation.
Example:Solve the equation 2x + 5 = 3x – 2.
- Simplify both sides: 2x + 5 – 2x = 3x – 2 – 2x
- Combine like terms: 5 = x – 2
- Add 2 to both sides: 5 + 2 = x – 2 + 2
- Simplify: 7 = x
Therefore, the solution to the equation 2x + 5 = 3x – 2 is x = 7.
Solving Inequalities with Variables on Both Sides, Glencoe algebra 1 chapter 4 answer key
An inequality with variables on both sides is an inequality in which the variable appears on both the left-hand side and the right-hand side of the inequality. To solve an inequality with variables on both sides, we need to isolate the variable on one side of the inequality.
Steps for Solving Inequalities with Variables on Both Sides:
- Simplify both sides of the inequality.
- Add or subtract the same number from both sides of the inequality.
- Multiply or divide both sides of the inequality by the same positive number.
- Multiply or divide both sides of the inequality by the same negative number and reverse the direction of the inequality.
- Continue simplifying until the variable is isolated on one side of the inequality.
Example:Solve the inequality 2x – 5 > 3x + 2.
- Simplify both sides: 2x – 5 – 3x > 3x + 2 – 3x
- Combine like terms: -x – 5 > 2
- Add 5 to both sides: -x – 5 + 5 > 2 + 5
- Simplify: -x > 7
- Multiply both sides by -1 and reverse the direction of the inequality: x< -7
Therefore, the solution to the inequality 2x – 5 > 3x + 2 is x< -7.
Solving Absolute Value Equations and Inequalities
An absolute value equation is an equation that contains an absolute value expression. An absolute value inequality is an inequality that contains an absolute value expression.
Steps for Solving Absolute Value Equations:
- Isolate the absolute value expression on one side of the equation.
- Set the expression inside the absolute value bars equal to both a positive and a negative number.
- Solve each equation separately.
- Check your solutions in the original equation.
Steps for Solving Absolute Value Inequalities:
- Isolate the absolute value expression on one side of the inequality.
- Set the expression inside the absolute value bars greater than or equal to zero.
- Solve the inequality.
- Check your solutions in the original inequality.
Example:Solve the absolute value equation |x – 3| = 5.
- Isolate the absolute value expression: x – 3 = 5 or x – 3 = -5
- Solve each equation: x = 8 or x = -2
- Check your solutions: |8 – 3| = 5 and |-2 – 3| = 5
Therefore, the solutions to the absolute value equation |x – 3| = 5 are x = 8 and x = -2.
Applications of Equations and Inequalities
Equations and inequalities are used in a wide variety of applications in everyday life. For example, equations can be used to calculate the area of a rectangle, the volume of a sphere, or the distance traveled by a car. Inequalities can be used to determine whether a number is greater than or less than another number, or to find the range of values that a variable can take.
Here are some examples of how equations and inequalities are used in real-world situations:
- A farmer has 100 feet of fencing to enclose a rectangular plot of land. What are the possible dimensions of the plot?
- A company wants to produce a box that has a volume of 100 cubic inches. What are the possible dimensions of the box?
- A car travels 200 miles in 4 hours. What is the average speed of the car?
Query Resolution: Glencoe Algebra 1 Chapter 4 Answer Key
What is the Glencoe Algebra 1 Chapter 4 Answer Key?
The Glencoe Algebra 1 Chapter 4 Answer Key is a comprehensive guide that provides solutions to the practice problems in Chapter 4 of the Glencoe Algebra 1 textbook.
What topics are covered in Chapter 4 of Glencoe Algebra 1?
Chapter 4 of Glencoe Algebra 1 covers solving equations with variables on both sides, solving inequalities with variables on both sides, solving absolute value equations and inequalities, and applications of equations and inequalities in real-world scenarios.
How can I use the Glencoe Algebra 1 Chapter 4 Answer Key?
The Glencoe Algebra 1 Chapter 4 Answer Key can be used to check your answers to practice problems, review concepts, and prepare for tests.
