Answer Key 2.2

  1. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{rrrrl} 5&+&\dfrac{n}{4}&=&\phantom{-}4 \\ -5&&&&-5 \\ \hline &&4 \left(\dfrac{n}{4}\right)&=&(-1)4 \\ \\ &&n&=&-4 \end{array}[/latex]
  2. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{rrlrr} -2&=&-2m&+&12 \\ -12&&&-&12 \\ \hline \dfrac{-14}{-2}&=&\dfrac{-2m}{-2}&& \\ \\ m&=&7&& \end{array}[/latex]
  3. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{rrrrr} 102&=&-7r&+&4 \\ -4&&&-&4 \\ \hline \dfrac{98}{-7}&=&\dfrac{-7r}{-7}&& \\ \\ r&=&-14&& \end{array}[/latex]
  4. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{rrrrr} 27&=&21&-&3x \\ -21&&-21&& \\ \hline \dfrac{6}{-3}&=&\dfrac{-3x}{-3}&& \\ \\ x&=&-2&& \end{array}[/latex]
  5. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{rrrrr} -8n&+&3&=&-77 \\ &-&3&&-3 \\ \hline &&\dfrac{-8n}{-8}&=&\dfrac{-80}{-8} \\ \\ &&n&=&10 \end{array}[/latex]
  6. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{rrrrl} -4&-&b&=&\phantom{+}8 \\ +4&&&&+4 \\ \hline &&(-b&=&\phantom{-}12)(-1) \\ &&b&=&-12 \end{array}[/latex]
  7. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{rrl} \dfrac{0}{-6}&=&\dfrac{-6v}{-6} \\ \\ v&=&0 \end{array}[/latex]
  8. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{rrcrl} -2&+&\dfrac{x}{2}&=&\phantom{+}4 \\ +2&&&&+2 \\ \hline &&2\left(\dfrac{x}{2}\right)&=&\phantom{+}(6)2 \\ \\ &&x&=&12 \end{array}[/latex]
  9. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{rrcrr} -8&=&\dfrac{x}{5}&-&6 \\ +6&&&+&6 \\ \hline 5(-2)&=&\left(\dfrac{x}{5}\right) 5&& \\ \\ x&=&-10&& \end{array}[/latex]
  10. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{rrcrr} -5&=&\dfrac{a}{4}&-&1 \\ +1&&&+&1 \\ \hline 4(-4)&=&\left(\dfrac{a}{4}\right) 4&& \\ \\ a&=&-16&& \end{array}[/latex]
  11. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{rrcrr} 0&=&-7&+&\dfrac{k}{2} \\ +7&&+7&& \\ \hline 2(7)&=&\left(\dfrac{k}{2}\right)2&& \\ \\ k&=&14&& \end{array}[/latex]
  12. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{rrrrr} -6&=&15&+&3p \\ -15&&-15&& \\ \hline \dfrac{-21}{3}&=&\dfrac{3p}{3}&& \\ \\ p&=&-7&& \end{array}[/latex]
  13. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{rrrrl} -12&+&3x&=&\phantom{+1}0 \\ +12&&&&+12 \\ \hline &&\dfrac{3x}{3}&=&\dfrac{12}{3} \\ \\ &&x&=&4 \end{array}[/latex]
  14. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{rrrrr} -5m&+&2&=&27 \\ &-&2&&-2 \\ \hline &&\dfrac{-5m}{-5}&=&\dfrac{25}{-5} \\ \\ &&m&=&-5 \end{array}[/latex]

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Intermediate Algebra by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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