1.4P: Practice

MTH 95: Algebra 3 · LibreTexts

0%

Contents

    Text

    Size
    100%
    Theme
    Typeface
    Line length
    Spacing

    From LibreTexts, under CC BY-NC 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    Practice Makes Progress

    Exercise

    Draw a number line, then plot the numbers \(4, 3, -4, \frac{7}{8}, -\frac{8}{3}\) on your number line. Label each point with its value. Finally, list the numbers in order, from smallest to largest.

     Solve each inequality algebraically, and write your solution in both interval notation and set-builder notation.

    Exercise

    \(x + 10 < 19\)

    Exercise

    \(4x < 8\)

    Exercise

    \(-2y \leq -2\)

    Exercise

    \(-5n - 6 \geq 4 - 9n\)

    Exercise

    \(15x + 5 < 6x + 2\)

    Exercise

    \(\frac{3}{2}x > \frac{9}{8}\)

    Exercise

    \(x + \frac{3}{2} < \frac{9}{5}\)

    Exercise

    \(\frac{4}{7} - \frac{1}{6}x \leq \frac{4}{3}x - \frac{1}{2}\)

    Exercise

    \(\frac{9}{7}y + \frac{9}{2} > \frac{1}{7}y + \frac{7}{2}\)

    Exercise

    \(6n - 12(3 - n) \leq 9(n - 4) + 9n\)

    Exercise

    \(\frac{4}{5}h - \frac{2}{3}(h - 9) > \frac{1}{15}(2h + 90)\)

    For each application problem,
    1. Define variables and write an inequality that represents the scenario
    2. Solve the inequality algebraically
    3. State the solution in the context of the problem. 

    Exercise

    Kimuyen needs to earn $4,150 per month to cover all her expenses. Her job pays her $3,475 per month plus 4% of her total sales. What is the minimum Kimuyen’s total sales must be for her to pay all her expenses?

    Exercise

    Nataly is considering two job offers. The first job would pay her $83,000 per year. The second would pay her $66,500 plus 15% of her total sales. What would her total sales need to be for her salary on the second offer to be higher than the first?

    Exercise

    Kellen wants to rent a banquet room in a restaurant for her cousin’s baby shower. The restaurant charges $350 for the banquet room plus $32.50 per person for lunch. How many people can Kellen have at the shower if she wants the maximum cost to be $1,500?

    Self-Check

    In this section, you practiced:

    1. Writing inequalities in interval notation
    2. Writing inequalities in set-builder notation
    3. Sketching inequalities on a number line
    4. Solving linear inequalities
    5. Writing an inequality to model a scenario
    6. Interpreting the solution to an inequality in context

    From the list of skills above:

    1. I can complete these independently without notes:
    1. I can complete these, but need to reference an example or other resource to help:
    1. I don’t understand these yet:

    It’s okay to not be fully confident with every skill yet! But it’s essential to continue making progress. Identify at least one step you will take to improve your understanding of the topics you listed in parts 2 or 3 above:

    • Visit the math lab
    • Contact my instructor
    • Re-work practice problems
    • Ask a classmate or friend for help

    Which step(s) from above did you complete after last week's textbook practice?

    This page titled 1.4P: Practice was last modified on Wed, 10 Dec 2025 03:24:01 GMT and is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Math Department.