Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

1. \(5x+13=12\)
2. \(9x-9=11\)
3. \(-9x+5=15\)
4. \(-5x+10=-6\)
5. \(2x-5=2\)
6. \(9x+2=-8\)
7. \(-x-6=-14\)
8. \(10x+3=-1\)
9. \(-3x+5=2\)
10. \(7x+15=-11\)
11. \(2x+1=14\)
12. \(12x+9=-12\)

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+13}& = &12 \\\Leftrightarrow & 5x \color{red}{+13}\color{blue}{-13} & = &12\color{blue}{-13} \\\Leftrightarrow &5x & = &-1\\\Leftrightarrow & \color{red}{5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{-9}& = &11 \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9} & = &11\color{blue}{+9} \\\Leftrightarrow &9x & = &20\\\Leftrightarrow & \color{red}{9}x & = &20\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{20}{9} \\\Leftrightarrow & \color{green}{ x = \frac{20}{9} } & & \\ & V = \left\{ \frac{20}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+5}& = &15 \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5} & = &15\color{blue}{-5} \\\Leftrightarrow &-9x & = &10\\\Leftrightarrow & \color{red}{-9}x & = &10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+10}& = &-6 \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10} & = &-6\color{blue}{-10} \\\Leftrightarrow &-5x & = &-16\\\Leftrightarrow & \color{red}{-5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-5}& = &2 \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5} & = &2\color{blue}{+5} \\\Leftrightarrow &2x & = &7\\\Leftrightarrow & \color{red}{2}x & = &7\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{7}{2} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+2}& = &-8 \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2} & = &-8\color{blue}{-2} \\\Leftrightarrow &9x & = &-10\\\Leftrightarrow & \color{red}{9}x & = &-10\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-10}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-6}& = &-14 \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6} & = &-14\color{blue}{+6} \\\Leftrightarrow &-x & = &-8\\\Leftrightarrow & \color{red}{-}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-8}{-1} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+3}& = &-1 \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3} & = &-1\color{blue}{-3} \\\Leftrightarrow &10x & = &-4\\\Leftrightarrow & \color{red}{10}x & = &-4\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-4}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{+5}& = &2 \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5} & = &2\color{blue}{-5} \\\Leftrightarrow &-3x & = &-3\\\Leftrightarrow & \color{red}{-3}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-3}{-3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+15}& = &-11 \\\Leftrightarrow & 7x \color{red}{+15}\color{blue}{-15} & = &-11\color{blue}{-15} \\\Leftrightarrow &7x & = &-26\\\Leftrightarrow & \color{red}{7}x & = &-26\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-26}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{7} } & & \\ & V = \left\{ \frac{-26}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{+1}& = &14 \\\Leftrightarrow & 2x \color{red}{+1}\color{blue}{-1} & = &14\color{blue}{-1} \\\Leftrightarrow &2x & = &13\\\Leftrightarrow & \color{red}{2}x & = &13\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{13}{2} \\\Leftrightarrow & \color{green}{ x = \frac{13}{2} } & & \\ & V = \left\{ \frac{13}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{+9}& = &-12 \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9} & = &-12\color{blue}{-9} \\\Leftrightarrow &12x & = &-21\\\Leftrightarrow & \color{red}{12}x & = &-21\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-21}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)