Practice Test Using ALEKS Software

Introduction

• This is a practice test printed on paper, meant to be done online in actual use.
• Suggestion: Write down the question, work it out, then compare with the solution given.
• Focus on following instructions carefully.

Solving Equations

Problem 1

• Equation: The sum of nine times a number and 4 equals 8.
  • Write it as: 9y + 4 = 8.
  • Solve for y.

Problem 2

• Equation: 9 = u + 5.
  • Subtract 5 from both sides.
  • Solution: u = -14.

Problem 3

• Equation: -5x = 10/3.
  • Multiply both sides by 3 to clear the fraction.
  • Simplify: -15x = 10.
  • Divide by -15: x = -2/3.

Problem 4

• Equation with fractions: Find the least common denominator (LCD) for 3, 2, and 9. LCD = 18.
  • Multiply each term by 18.
  • Simplify: -6 - 27y = 10.
  • Transpose and solve: y = -16/27.

Problem 5

• Equation with fractions: Find the LCD for denominators 4 and 1. LCD = 4.
  • Multiply each term by 4.
  • Simplify and solve: y = 76.

Problem 6

• Equation: Get rid of grouping symbols, distribute.
  • Simplify: 8y - 18 = 14.
  • Transpose and solve: y = 4.

Problem 7

• Equation with three terms: Find the LCD for denominators 5, 7, and 2. LCD = 70.
  • Multiply each term by 70.
  • Simplify and solve: x = 5/28.

Problem 8

• Equation: Identify two terms.
  • Multiply by LCD = -3.
  • Simplify and solve: x = 8.

Problem 9

• Equation with four terms: Find the LCD for denominators 3, 5, 15. LCD = 15.
  • Multiply each term by 15.
  • Simplify and solve: w = 63/2.

Application Problems

Problem 10

• Word Problem: Adult and student tickets sold.
  • Set up equation: A + 3A = 360.
  • Solve for A: A = 90.

Problem 11

• Equation with fractions: Combine like terms and solve.
  • Simplify: u = 4.

Problem 12

• Word Problem: Total distance walked in two weeks.
  • Combine distances: 271 + V.

Problem 13

• Percentage Problem: Price reduced by 45%.
  • Shortcut: 55% of original price.
  • Calculate: Price = $33.

Problem 14

• Percentage of deliveries completed.
  • Formula: (19/25) * 100 = 76%.*

Problem 15

• Percentage Problems:
  • What percent of 60 is 57? (57/60) * 100 = 95%
  • What number is 15% of 80? 0.15 * 80 = 12.

Problem 16

• Speed and Distance Problem: Find time.
  • Formula: Distance = Rate * Time.
  • Calculate: Time = 1.25 minutes.*

Problem 17

• Average/Mean Calculation: Find required score for certain average.
  • Combine and solve: Required score = 66.

Inequalities

Problem 18

• Write inequalities:
  • 10% discount for spending >= $100: D >= 100
  • Luggage weight <= 55 lbs: W <= 55

Problem 19

• Graph inequalities on number line:
  • Example: (-7, -4).

Problem 20

• Solve inequality with fractions:
  • Multiply by LCD = 30.
  • Simplify and solve: W >= -23/30.

Conclusion

• Practice involves solving different types of equations and inequalities.
• Ensure steps are clear and logical.
• Use multiplication to clear fractions and ensure correct variable isolation.
• Verify work by checking the correct copying and solving steps.