Answer Key 2.2

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

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