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5.11: Proficiency Exam

  • Page ID
    58543
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    Proficiency Exam

    Solve the equations and inequalities for the following problems.

    Exercise \(\PageIndex{1}\)

    \(x+8=14\)

    Answer

    \(x=6\)

    Exercise \(\PageIndex{2}\)

    \(6a+3=−10\)

    Answer

    \(a = \dfrac{-13}{6}\)

    Exercise \(\PageIndex{3}\)

    \(\dfrac{-3a}{8} = 6\)

    Answer

    \(a=−16\)

    Exercise \(\PageIndex{4}\)

    \(\dfrac{x}{-2} + 16 = 11\)

    Answer

    \(x=10\)

    Exercise \(\PageIndex{5}\)

    \(\dfrac{y-9}{4} + 6 = 3\)

    Answer

    \(y=−3\)

    Exercise \(\PageIndex{6}\)

    \(5b−8=7b+12\)

    Answer

    \(b=−10\)

    Exercise \(\PageIndex{7}\)

    \(3(2a+4)=2(a+3)\)

    Answer

    \(a = -\dfrac{3}{2}\)

    Exercise \(\PageIndex{8}\)

    \(5(y+3)−(2y−1)=−5\)

    Answer

    \(y=−7\)

    Exercise \(\PageIndex{9}\)

    \(\dfrac{-(4x+3-5x)}{3} = 2\)

    Answer

    \(x=9\)

    Exercise \(\PageIndex{10}\)

    Solve \(2p−6q+1=−2\) for \(p\).

    Answer

    \(p = \dfrac{6q-3}{2}\)

    Exercise \(\PageIndex{11}\)

    Solve \(p = \dfrac{nRT}{V}\) for \(T\)

    Answer

    \(T = \dfrac{Vp}{nR}\)

    Exercise \(\PageIndex{12}\)

    \(a−8≥4\)

    Answer

    \(a≥12\)

    Exercise \(\PageIndex{13}\)

    \(−3a+1<−5\)

    Answer

    \(a>2\)

    Exercise \(\PageIndex{14}\)

    \(−2(a+6)≤−a+11\)

    Answer

    \(a≥−23\)

    Exercise \(\PageIndex{15}\)

    \(\dfrac{-4x-3}{3} > -9\)

    Answer

    \(x<6\)

    Translate the phrases or sentences into mathematical expressions or equations for the following problems.

    Exercise \(\PageIndex{16}\)

    Three added to twice a number.

    Answer

    \(3+2a\)

    Exercise \(\PageIndex{17}\)

    Eight less than two thirds of a number.

    Answer

    \(\dfrac{2}{3}x - 8\)

    Exercise \(\PageIndex{18}\)

    Two more than four times a number.

    Answer

    \(2+4x\)

    Exercise \(\PageIndex{19}\)

    A number is added to itself and this result is multiplied by the original number cubed. The result is twelve.

    Answer

    \(2x(x^3) = 12\)

    Exercise \(\PageIndex{20}\)

    A number is decreased by five and that result is divided by ten more than the original number. The result is six times the original number.

    Answer

    \(\dfrac{x-5}{x+10} = 6x\)

    Solve the following problems.

    Exercise \(\PageIndex{21}\)

    Eight percent of a number is 1.2. What is the number?

    Answer

    \(x=15\)

    Exercise \(\PageIndex{22}\)

    Three consecutive odd integers sum to 38. What are they?

    Answer

    There are no three consecutive odd integers that add to 38.

    Exercise \(\PageIndex{23}\)

    Five more than three times a number is strictly less than seventeen. What is the number?

    Answer

    \(x<4\)

    Exercise \(\PageIndex{24}\)

    Solve \(y=8x−11\) for \(y\) if \(x=3\), and write the solution as an ordered pair.

    Answer

    \((3,13)\)


    This page titled 5.11: Proficiency Exam is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Denny Burzynski & Wade Ellis, Jr. (OpenStax CNX) .

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