Answer Key 3.7

Terrance Berg

Answer Key 3.7

$2x+5=25$
$4x+12=36$
$3x-8=22$
$6x-8=22$
$x-8=\dfrac{x}{2}$
$x-4=\dfrac{x}{2}$
$x+x+1+x+2=21$
$x+x+2-(x+4)=5$
$\begin{array}{rrrrrr} \\ \\ \\ \\ \\ 5&+&3x&=&17& \\ -5&&&&-5& \\ \midrule &&3x&=&12& \\ \\ &&x&=&\dfrac{12}{3}&\text{or } 4 \end{array}$
$\begin{array}{rrrrrr} \\ \\ \\ \\ \\ 3x&-&5&=&10& \\ &+&5&&+5& \\ \midrule &&3x&=&15& \\ \\ &&x&=&\dfrac{15}{3}&\text{or } 5 \end{array}$
$\begin{array}{rrrrrrr} \\ \\ 60&+&9x&=&10x&-&2 \\ +2&-&9x&&-9x&+&2 \\ \midrule &&62&=&x&& \end{array}$
$\begin{array}{rrrrrrr} \\ \\ 7x&-&11&=&6x&+&5 \\ -6x&+&11&&-6x&+&11 \\ \midrule &&x&=&16&& \end{array}$
$\begin{array}{rrrrrrrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ x&+&x&+&1&+&x&+&2&=&108 \\ &&&&&&3x&+&3&=&108 \\ &&&&&&&-&3&&-3 \\ \midrule &&&&&&&&3x&=&105 \\ \\ &&&&&&&&x&=&\dfrac{105}{3}\text{ or }35 \\ \\ &&&&&&&&&\therefore &35, 36, 37 \end{array}$
$\begin{array}{rrrrrrrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ x&+&x&+&1&+&x&+&2&=&-126 \\ &&&&&&3x&+&3&=&-126 \\ &&&&&&&-&3&&-\phantom{00}3 \\ \midrule &&&&&&&&3x&=&-129 \\ \\ &&&&&&&&x&=&\dfrac{-129}{3}\text{ or }-43 \\ \\ &&&&&&&&&\therefore &-43, -42, -41 \end{array}$
$\begin{array}{rrrrrrrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ \\ x&+&2(x&+&1)&+&3(x&+&2)&=&-76 \\ x&+&2x&+&2&+&3x&+&6&=&-76 \\ &&&&&&6x&+&8&=&-76 \\ &&&&&&&-&8&&-\phantom{0}8 \\ \midrule &&&&&&&&6x&=&-84 \\ \\ &&&&&&&&x&=&\dfrac{-84}{6}\text{ or }-14 \\ \\ &&&&&&&&&\therefore &-14, -13, -12 \end{array}$
$\begin{array}{rrrrrrrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ \\ x&+&2(x&+&2)&+&3(x&+&4)&=&\phantom{0}70 \\ x&+&2x&+&4&+&3x&+&12&=&\phantom{0}70 \\ &&&&&&6x&+&16&=&\phantom{0}70 \\ &&&&&&&-&16&&-16 \\ \midrule &&&&&&&&6x&=&54 \\ \\ &&&&&&&&x&=&\dfrac{54}{6}\text{ or }9 \\ \\ &&&&&&&&&\therefore &9,11,13 \end{array}$

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