Section 0.3P: Practice

MTH 65: Algebra 2 · LibreTexts

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    Practice Makes Progress

    In the following exercises, determine whether the given values are solutions to the equation.

    Exercise

    \(6y+10=12y\)

    1. \(y=\dfrac{5}{3}\)
    2. \(y=-\dfrac{1}{2}\)
    Exercise

    \(8u-1=6u\)

    1. \(u=-\dfrac{1}{2}\)
    2. \(u=\dfrac{1}{2}\)

    In the following exercises, solve each linear equation.

    Exercise

    \(15(y-9)=-60\)

    Exercise

    \(-(w-12)=30\)

    Exercise

    \(51+5(4-q)=56\)

    Exercise

    \(\dfrac{2}{3}(9c-3)=22\)

    Exercise

    \(12+2(5-3y)=-9(y-1)-2\)

    Exercise

    \(4(p-4)-(p+7)=5(p-3)\)

    Exercise

    \(4[5-8(4c-3)]=12(1-13c)-8\)

    Exercise

    \(5[2(m+4)+8(m-7)]=2[3(5+m)-(21-3m)]\)

    In the following exercises, solve each equation.

    Exercise

    \(\dfrac{1}{4}x-\dfrac{1}{2}=-\dfrac{3}{4}\)

    Exercise

    \(\dfrac{1}{2}a+\dfrac{3}{8}=\dfrac{3}{4}\)

    Exercise

    \(\dfrac{1}{3}w+\dfrac{5}{4}=w-\dfrac{1}{4}\)

    Exercise

    \(\dfrac{1}{4}(p-7)=\dfrac{1}{3}(p+5)\)

    Exercise

    \(\dfrac{4n+8}{4}=\dfrac{n}{3}\)

    Exercise

    \(\dfrac{7u-1}{4}-1=\dfrac{4u+8}{5}\)

    Exercise

    \(0.4x+0.6=0.5x-1.2\)

    Exercise

    \(0.05n+0.10(n+8)=2.15\)

    Exercise

    \(0.10d+0.25(d+5)=4.05\)

    In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction, and then state the solution.

    Exercise

    \(23z+19=3(5z-9)+8z+46\)

    Exercise

    \(18(5j-1)+29=47\)

    Exercise

    \(7v+42=11(3v+8)-2(13v-1)\)

    Exercise

    \(9(14d+9)+4d=13(10d+6)+3\)

    Everyday Math

    Exercise

    Fencing Micah has 74 feet of fencing to make a dog run in his yard. He wants the length to be 2.5 feet more than the width. Find the length, L, by solving the equation \(2L+2(L-2.5)=74\).

    Writing Exercises

    Exercise

    What is the first step you take when solving the equation \(3-7(y-4)=38?\) Why is this your first step?

    Exercise

    If an equation has fractions only on one side, why do you have to multiply both sides of the equation by the LCD?

    Self Check

    Use this checklist to evaluate your mastery of the objectives of this section.

    This table has four columns and four rows. The first row is a header and it labels each column, “I can…”, “Confidently,” “With some help,” and “No-I don’t get it!” In row 2, the I can was solve linear equations using a general strategy. In row 3, the I can was classify equations. In row 4, the I can was solve equations with fraction or decimal coefficients.

    If most of your checks were:

    …confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them.

    …with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is crucial to establish a strong foundation before proceeding. Who can you ask for help? Your classmates, tutors, and class instructor are good resources.

    …no - I don’t get it! This is a warning sign, and you must not ignore it. You should get help right away, or you will quickly be overwhelmed. Meet with your instructor during their drop-in hours as soon as you can to discuss your situation. Together, you can devise a plan to get the help you need.

    This page titled Section 0.3P: Practice was last modified on Wed, 27 Aug 2025 19:09:20 GMT and is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Math Department.