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Chapter Analysis
Beginner7 pages • EnglishQuick Summary
The chapter focuses on linear equations in one variable, explaining that these are equations where the highest power of the variable is one. It covers concepts such as the equality of values on both sides of an equation and methodologies to solve equations with the variable on both sides. The chapter also demonstrates how to simplify expressions to solve complex equations and illustrates real-world applications such as problems involving ages and perimeters.
Key Topics
- •Definition of linear equations
- •Solving linear equations with variable on both sides
- •Simplification of complex equations
- •Applications of linear equations
- •Transposing terms in equations
Learning Objectives
- ✓Understand the structure of linear equations
- ✓Master solving equations with variables on both sides
- ✓Learn methods to simplify complex expressions
- ✓Recognize and apply linear equations to real-world scenarios
- ✓Develop skills in transposing terms within equations
Questions in Chapter
Solve the following equations and check your results. 1. 3x = 2x + 18
Page 17
Solve the following linear equations. 1. 1/(2x - 1/4) = 1/(2x + 5/3) - 41/10
Page 20
Additional Practice Questions
Solve for x: 7x - 5 = 3x + 11
easyAnswer: Add 5 to both sides to get 7x = 3x + 16. Then subtract 3x from both sides to get 4x = 16. Finally, divide by 4 on both sides to solve for x, yielding x = 4.
If 5x + 3 = 18, find the value of x.
easyAnswer: Subtract 3 from both sides to get 5x = 15. Divide both sides by 5 to find x = 3.
What is the solution of the equation 2(x + 3) = x + 9?
mediumAnswer: Expand the left-hand side to get 2x + 6 = x + 9. Subtract x from both sides to get x + 6 = 9. Finally, subtract 6 from both sides to solve for x, resulting in x = 3.
A number minus 5 is equal to twice the same number. Find the number.
mediumAnswer: Let the number be x. Then, x - 5 = 2x. Subtract x from both sides to get -5 = x. Thus, x = -5.
Solve (x/3) + (x/4) = 7
hardAnswer: First find a common denominator for the fractions, which is 12. This converts the equation to (4x/12) + (3x/12) = 7. Combine to get (7x/12) = 7. Multiply both sides by 12 to solve for x, yielding x = 12.