Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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