📚 Part 1: Identifying Components and Writing Equations

1. In the equation 4x + 7 = 23, identify each component:

Coefficient: _________ Variable: _________ Constant: _________

2. Write a linear equation for this word problem: "Five times a number decreased by 8 equals 17."

3. Which equation correctly represents "Three more than twice a number is 15"?

2x + 3 = 15

3x + 2 = 15

2x - 3 = 15

3 + x = 15

4. Write an equation for: "The cost of renting a car is $25 per day plus a $40 fee. The total cost is $115."

✏️ Part 2: Solving Linear Equations

5. Solve: 3x + 8 = 26

Show all steps and justify each operation:

6. Solve: 2x - 5 = 4x + 3

Show your work step by step:

7. Solve: (x + 4)/3 = 7

8. Check which values are solutions to 2x + 1 = 9:

x = 4

x = 5

x = 3

x = 2

9. Sarah has $150 in her savings account. She saves $20 each week. Write and solve an equation to find when she'll have $270.

Equation: _________________________

Solution: _________________________

10. Solve by factoring: x² - 7x + 12 = 0

11. Explain in your own words: How do coefficients affect the solution process when solving linear equations?