College Algebra

  • 1. Perform the following operation with real numbers.
  • 9 − 16
  • 2. Perform the following operation with real numbers.
  •  -6.3/ 0.7
  • 3. Simplify the numerical expression.
  • 3(5 − 9) − 3(−9)
  • 4. Write a numerical statement to represent the problem. Then simplify the numerical expression to answer the question.
    After dieting for 60 days, Ignacio has lost 42 pounds. What number describes his average weight change per day?
  • Ignacio lost an average of ___ pounds per day.
  • 5. Simplify the algebraic expression by removing parentheses and combining similar terms.
  • 5(2x + 1) + 6(3x − 2)
  • 6. Evaluate the algebraic expression for the given values of the variables.
  • 4xy − x2y2 + 2y2, x = 8 and y = −1
  • 7. Solve the equation. (If all real numbers are solutions, enter REALS. Enter EMPTY for the empty set.)
  • 3x + 2 = 5x – 8
  • X=___
  • 8. Solve the equation. (If all real numbers are solutions, enter REALS. Enter EMPTY for the empty set.)
  • −2(5x + 9) = −5(4x + 1)
  • X=___
  • 9. Use an algebraic approach to solve the problem.
    Angelo is paid double time for each hour he works over 40 hours in a week. Last week he worked 44 hours and earned $528. What is his normal hourly rate?
  • ___ dollars per hour
  • 10.  Use the formula to solve for the given variable.
    Solve i = Prt for t, given that P = $1350, r = 4%, and i = $216.
  •   t = ___yr.
  • 11. Solve the following for the indicated variable.
  • A = ½ h (b1 + b2) for h (Area of a trapezoid)
  • h=___
  • 12. Solve the inequality.
  • x − 4 > −1
  • ___
  • Graph the solution set on a number line.
  • 13. Solve the inequality.
  • 5x + 6 ≥ 4x + 9
  • ___
  • Graph the solution set on a number line.
  • 14. Graph the solution set for the compound inequality.
  • x > 3 or x < 5
  • Express the solution set in interval notation. (Enter EMPTY or ∅ for the empty set.) ___
  • 15. Solve the compound inequality and graph the solution set.
  • x + 5 > −4    and    x + 5 < 4
  • Express the solution set in interval notation. ___
  • 16. Solve the problem by setting up and solving an appropriate inequality.
    Thanh has scores of 54, 82, 68, and 72 on his first four math exams. What score must he make on the fifth exam to have an average of 70 or better for the five exams?
  • ___or better
  • 17. Solve the equation.
  • |x − 7| = 8
  • X=___ (smaller value)
  • X=___ (larger value)
  • 18. Solve the inequality. (Enter your answer using interval notation.)
  • |x − 1| < 7
  • ___
  • Graph the solution.
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