21122中２・式の計算・計算問題・等式の変形2

(1)   $S=2\pi rh\quad[\;r\;]$

$\begin{eqnarray}\quad\;\;S&=&2\pi rh\\[6pt]2\pi rh&=&S\\[6pt]2\pi rh \color{red} \div 2\pi h&=&S \color{red} \div 2\pi h\\[6pt]r&=&\dfrac{\;S\;}{\;2 \pi h\;}\end{eqnarray}\;\;$

答$r=\dfrac{\;S\;}{\;2 \pi h\;}$

(2)   $S=\dfrac{1}{\;2\;}(\,a+b\,)h\quad[\;a\;]$

$\begin{eqnarray}\quad\;\;S&=&\dfrac{1}{\;2\;}(\,a+b\,)h\\[6pt]\dfrac{1}{\;2\;}(\,a+b\,)h&=&S\\[6pt]\dfrac{1}{\;2\;}(\,a+b\,)h \color{red}\times 2&=&S \color{red}\times 2\\[6pt](\,a+b\,)h&=&2S\\[6pt](\,a+b\,)h \color{red}\div h&=&2S \color{red}\div h\\[6pt]a+b&=&\dfrac{\;2S\;}{h}\\[6pt]a&=&\dfrac{\;2S\;}{h}-b\end{eqnarray}\;\;$

答$a=\dfrac{\;2S\;}{h}-b$

(3)   $\ell=2(\,3a+5b\,)\quad[\;b\;]$

$\begin{eqnarray}\quad\;\;\ell&=&2(\,3a+5b\,)\\[6pt]2(\,3a+5b\,)&=&\ell\\[6pt]2(\,3a+5b\,) \color{red}\div 2&=&\ell \color{red}\div 2\\[6pt]3a+5b&=&\dfrac{\;\ell\;}{\;2\;}\\[6pt]5b&=&\dfrac{\;\ell\;}{\;2\;}-3a\\[6pt]5b \color{red}\times \dfrac{\;1\;}{5}&=&\Bigl(\,\dfrac{\;\ell\;}{\;2\;}-3a\,\Bigr) \color{red}\times \dfrac{\;1\;}{5}\\[6pt]b&=&\dfrac{\;\ell\;}{\;10\;}-\dfrac{\;3\;}{5}a\end{eqnarray}\;\;$

答$b=\dfrac{\;\ell\;}{\;10\;}-\dfrac{\;3\;}{5}a$

(4)   $\dfrac{\;x-5y\;}{\;3\;}=-x-1\quad[\;y\;]$

$\begin{eqnarray}\quad\;\;\dfrac{\;x-5y\;}{\;3\;}&=&-x-1\\[6pt]\dfrac{\;x-5y\;}{\;3\;} \color{red} \times 3&=&(\,-x-1\,) \color{red} \times 3\\[6pt]x-5y&=&-3x-3\\[6pt]-5y&=&-3x \color{red}-x\color{black}-3\\[6pt]-5y&=&-4x-3 \\[6pt]-5y \color{red}\times (\,-1\,)&=&(\,-4x-3\,) \color{red}\times (\,-1\,) \\[6pt]5y&=&4x+3\\[6pt]5y \color{red} \div 5 &=&(\,4x+3\,) \color{red} \div 5\\[6pt]y&=&\dfrac{\;4x+3\;}{5}\end{eqnarray}\;\;$

答$c=\dfrac{\;a-2b-10\;}{3}$

(5)   $a=\dfrac{\;c\;}{\;2-b\;}\quad[\;b\;]$

$\begin{eqnarray}\quad\;\;a&=&\dfrac{\;c\;}{\;2-b\;}\\[6pt]a \color{red} \times (\,2-b\,)&=&\dfrac{\;c\;}{\;2-b\;} \color{red} \times (\,2-b\,)\\[6pt]a(\,2-b\,)&=&c\\[6pt]a(\,2-b\,) \color{red} \div a&=&c\color{red} \div a\\[6pt]2-b&=&\dfrac{\;c\;}{\;a\;}\\[6pt]-b&=&\dfrac{\;c\;}{\;a\;}-2\\[6pt]-b \color{red} \times (\,-1\,)&=&\Bigl(\, \dfrac{c}{\;a\;}-2 \,\Bigr)\color{red} \times (\,-1\,)\\[6pt]b&=&-\dfrac{\;c\;}{a}+2\end{eqnarray}\;\;$

答$b=-\dfrac{\;c\;}{a}+2$