Liga cada equação à sua solução
Equações do 1.º grau: Matematicamente Falando 8 - Parte 2 Pág. 61 Ex. 1
Liga cada equação à sua solução:
| 1 | \[(x-7)-(3x+2)=9\] | A | \[2,7\] |
| 2 | \[\frac{x+3}{2}=\frac{x-5}{3}\] | B | \[-19\] |
| 3 | \[\frac{2}{3}(a+1)=\frac{a}{6}\] | C | \[-9\] |
| 4 | \[6x-\frac{3}{2}=5x+\frac{6}{5}\] | D | \[-\frac{4}{5}\] |
| 5 | \[b-\frac{1}{3}(b-1)=\frac{b}{4}\] | E | \[-\frac{4}{3}\] |
\[\begin{array}{*{35}{l}}
(x-7)-(3x+2)=9 & \Leftrightarrow & x-7-3x-2=9 \\
{} & \Leftrightarrow & -2x=18 \\
{} & \Leftrightarrow & x=-9 \\
\end{array}\]
\[\begin{array}{*{35}{l}}
\frac{x+3}{\underset{(3)}{\mathop{2}}\,}=\frac{x-5}{\underset{(2)}{\mathop{3}}\,} & \Leftrightarrow & 3x+9=2x-10 \\
{} & \Leftrightarrow & x=-19 \\
\end{array}\]
\[\begin{array}{*{35}{l}}
\frac{2}{3}(a+1)=\frac{a}{6} & \Leftrightarrow & \frac{2a}{\underset{(2)}{\mathop{3}}\,}+\frac{2}{\underset{(2)}{\mathop{3}}\,}=\frac{a}{\underset{(1)}{\mathop{6}}\,} \\
{} & \Leftrightarrow & 4a+4=a \\
{} & \Leftrightarrow & 3a=-4 \\
{} & \Leftrightarrow & a=-\frac{4}{3} \\
\end{array}\]
\[\begin{array}{*{35}{l}}
\underset{(10)}{\mathop{6x}}\,-\frac{3}{\underset{(5)}{\mathop{2}}\,}=\underset{(10)}{\mathop{5x}}\,+\frac{6}{\underset{(2)}{\mathop{5}}\,} & \Leftrightarrow & 60x-15=50x+12 \\
{} & \Leftrightarrow & 10x=27 \\
{} & \Leftrightarrow & x=2,7 \\
\end{array}\]
\[\begin{array}{*{35}{l}}
b-\frac{1}{3}(b-1)=\frac{b}{4} & \Leftrightarrow & \underset{(12)}{\mathop{b}}\,-\frac{b}{\underset{(4)}{\mathop{3}}\,}+\frac{1}{\underset{(4)}{\mathop{3}}\,}=\frac{b}{\underset{(3)}{\mathop{4}}\,} \\
{} & \Leftrightarrow & 12b-4b+4=3b \\
{} & \Leftrightarrow & 5b=-4 \\
{} & \Leftrightarrow & b=-\frac{4}{5} \\
\end{array}\]
| 1 | 2 | 3 | 4 | 5 |
| C | B | E | A | D |
