Answer Key 3.7
- \(2x+5=25\)
- \(4x+12=36\)
- \(3x-8=22\)
- \(6x-8=22\)
- \(x-8=\dfrac{x}{2}\)
- \(x-4=\dfrac{x}{2}\)
- \(x+x+1+x+2=21\)
- \(x+x+2-(x+4)=5\)
- \(\begin{array}{rrrrrr}
\\ \\ \\ \\ \\
5&+&3x&=&17& \\
-5&&&&-5& \\
\hline
&&3x&=&12& \\ \\
&&x&=&\dfrac{12}{3}&\text{or } 4
\end{array}\) - \(\begin{array}{rrrrrr}
\\ \\ \\ \\ \\
3x&-&5&=&10& \\
&+&5&&+5& \\
\hline
&&3x&=&15& \\ \\
&&x&=&\dfrac{15}{3}&\text{or } 5
\end{array}\) - \(\begin{array}{rrrrrrr}
\\ \\
60&+&9x&=&10x&-&2 \\
+2&-&9x&&-9x&+&2 \\
\hline
&&62&=&x&&
\end{array}\) - \(\begin{array}{rrrrrrr}
\\ \\
7x&-&11&=&6x&+&5 \\
-6x&+&11&&-6x&+&11 \\
\hline
&&x&=&16&&
\end{array}\) - \(\begin{array}{rrrrrrrrrrl}
\\ \\ \\ \\ \\ \\ \\ \\
x&+&x&+&1&+&x&+&2&=&108 \\
&&&&&&3x&+&3&=&108 \\
&&&&&&&-&3&&-3 \\
\hline
&&&&&&&&3x&=&105 \\ \\
&&&&&&&&x&=&\dfrac{105}{3}\text{ or }35 \\ \\
&&&&&&&&&\therefore &35, 36, 37
\end{array}\) - \(\begin{array}{rrrrrrrrrrl}
\\ \\ \\ \\ \\ \\ \\ \\
x&+&x&+&1&+&x&+&2&=&-126 \\
&&&&&&3x&+&3&=&-126 \\
&&&&&&&-&3&&-\phantom{00}3 \\
\hline
&&&&&&&&3x&=&-129 \\ \\
&&&&&&&&x&=&\dfrac{-129}{3}\text{ or }-43 \\ \\
&&&&&&&&&\therefore &-43, -42, -41
\end{array}\) - \(\begin{array}{rrrrrrrrrrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\
x&+&2(x&+&1)&+&3(x&+&2)&=&-76 \\
x&+&2x&+&2&+&3x&+&6&=&-76 \\
&&&&&&6x&+&8&=&-76 \\
&&&&&&&-&8&&-\phantom{0}8 \\
\hline
&&&&&&&&6x&=&-84 \\ \\
&&&&&&&&x&=&\dfrac{-84}{6}\text{ or }-14 \\ \\
&&&&&&&&&\therefore &-14, -13, -12
\end{array}\) - \(\begin{array}{rrrrrrrrrrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\
x&+&2(x&+&2)&+&3(x&+&4)&=&\phantom{0}70 \\
x&+&2x&+&4&+&3x&+&12&=&\phantom{0}70 \\
&&&&&&6x&+&16&=&\phantom{0}70 \\
&&&&&&&-&16&&-16 \\
\hline
&&&&&&&&6x&=&54 \\ \\
&&&&&&&&x&=&\dfrac{54}{6}\text{ or }9 \\ \\
&&&&&&&&&\therefore &9,11,13
\end{array}\)
