Beginning & Intermediate Algebra
Which of the following best describes the fundamental difference between the solution to a linear equation (e.g., ax+b=cax + b = c) and a linear inequality (e.g., ax+b>cax + b > c)?
Solve the inequality 2(x−3)+x≤82(x - 3) + x \(\le\) 8 and show the steps to isolate xx.
Solve the inequality 2(x+4)−32x<5+x4\(\displaystyle\) 2(x + 4) - \(\frac{3}{2}\)x < 5 + \(\frac{x}{4}\) for xx.
A student starts with the inequality x>4x > 4. They multiply both sides by −1-1 and write the result as −x>−4-x > -4. Evaluate whether the student's transformation is correct and provide the proper result if not.
A storage company charges a one-time setup fee of \(35\$35 and a monthly fee of \)20\$20. You want the total cost to be strictly less than $200\$200. Let mm be the number of months. Set up the inequality and determine the maximum whole number of full months you can rent storage.