Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{-7}& = &14 \\\Leftrightarrow & -14x \color{red}{-7}\color{blue}{+7} & = &14\color{blue}{+7} \\\Leftrightarrow &-14x & = &21\\\Leftrightarrow & \color{red}{-14}x & = &21\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{21}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+13}& = &-3 \\\Leftrightarrow & -13x \color{red}{+13}\color{blue}{-13} & = &-3\color{blue}{-13} \\\Leftrightarrow &-13x & = &-16\\\Leftrightarrow & \color{red}{-13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-16}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{16}{13} } & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+9}& = &15 \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9} & = &15\color{blue}{-9} \\\Leftrightarrow &4x & = &6\\\Leftrightarrow & \color{red}{4}x & = &6\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{6}{4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+14}& = &15 \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14} & = &15\color{blue}{-14} \\\Leftrightarrow &15x & = &1\\\Leftrightarrow & \color{red}{15}x & = &1\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{1}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{-12}& = &-10 \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12} & = &-10\color{blue}{+12} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+6}& = &10 \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6} & = &10\color{blue}{-6} \\\Leftrightarrow &15x & = &4\\\Leftrightarrow & \color{red}{15}x & = &4\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{4}{15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+3}& = &3 \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3} & = &3\color{blue}{-3} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{-2}& = &-4 \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2} & = &-4\color{blue}{+2} \\\Leftrightarrow &-3x & = &-2\\\Leftrightarrow & \color{red}{-3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+6}& = &-6 \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6} & = &-6\color{blue}{-6} \\\Leftrightarrow &9x & = &-12\\\Leftrightarrow & \color{red}{9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-12}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-4}& = &-2 \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4} & = &-2\color{blue}{+4} \\\Leftrightarrow &14x & = &2\\\Leftrightarrow & \color{red}{14}x & = &2\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{2}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-10}& = &-8 \\\Leftrightarrow & x \color{red}{-10}\color{blue}{+10} & = &-8\color{blue}{+10} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-10}& = &-15 \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10} & = &-15\color{blue}{+10} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)