Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-14}& = &1 \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14} & = &1\color{blue}{+14} \\\Leftrightarrow &4x & = &15\\\Leftrightarrow & \color{red}{4}x & = &15\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{15}{4} \\\Leftrightarrow & \color{green}{ x = \frac{15}{4} } & & \\ & V = \left\{ \frac{15}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-13}& = &3 \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13} & = &3\color{blue}{+13} \\\Leftrightarrow &12x & = &16\\\Leftrightarrow & \color{red}{12}x & = &16\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{16}{12} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{-3}& = &-2 \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3} & = &-2\color{blue}{+3} \\\Leftrightarrow &13x & = &1\\\Leftrightarrow & \color{red}{13}x & = &1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-10}& = &9 \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10} & = &9\color{blue}{+10} \\\Leftrightarrow &11x & = &19\\\Leftrightarrow & \color{red}{11}x & = &19\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{19}{11} \\\Leftrightarrow & \color{green}{ x = \frac{19}{11} } & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+11}& = &8 \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11} & = &8\color{blue}{-11} \\\Leftrightarrow &-6x & = &-3\\\Leftrightarrow & \color{red}{-6}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+1}& = &11 \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1} & = &11\color{blue}{-1} \\\Leftrightarrow &-9x & = &10\\\Leftrightarrow & \color{red}{-9}x & = &10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{-7}& = &-12 \\\Leftrightarrow & 15x \color{red}{-7}\color{blue}{+7} & = &-12\color{blue}{+7} \\\Leftrightarrow &15x & = &-5\\\Leftrightarrow & \color{red}{15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-5}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+14}& = &-13 \\\Leftrightarrow & -11x \color{red}{+14}\color{blue}{-14} & = &-13\color{blue}{-14} \\\Leftrightarrow &-11x & = &-27\\\Leftrightarrow & \color{red}{-11}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-27}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{27}{11} } & & \\ & V = \left\{ \frac{27}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-12}& = &-2 \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12} & = &-2\color{blue}{+12} \\\Leftrightarrow &4x & = &10\\\Leftrightarrow & \color{red}{4}x & = &10\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{10}{4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-10}& = &4 \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10} & = &4\color{blue}{+10} \\\Leftrightarrow &-6x & = &14\\\Leftrightarrow & \color{red}{-6}x & = &14\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{14}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-13}& = &-12 \\\Leftrightarrow & 13x \color{red}{-13}\color{blue}{+13} & = &-12\color{blue}{+13} \\\Leftrightarrow &13x & = &1\\\Leftrightarrow & \color{red}{13}x & = &1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{+4}& = &-8 \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4} & = &-8\color{blue}{-4} \\\Leftrightarrow &12x & = &-12\\\Leftrightarrow & \color{red}{12}x & = &-12\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-12}{12} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)