Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-5}& = &-10 \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5} & = &-10\color{blue}{+5} \\\Leftrightarrow &15x & = &-5\\\Leftrightarrow & \color{red}{15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-5}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+10}& = &-12 \\\Leftrightarrow & -4x \color{red}{+10}\color{blue}{-10} & = &-12\color{blue}{-10} \\\Leftrightarrow &-4x & = &-22\\\Leftrightarrow & \color{red}{-4}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-22}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+14}& = &12 \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14} & = &12\color{blue}{-14} \\\Leftrightarrow &3x & = &-2\\\Leftrightarrow & \color{red}{3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+7}& = &15 \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7} & = &15\color{blue}{-7} \\\Leftrightarrow &12x & = &8\\\Leftrightarrow & \color{red}{12}x & = &8\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{8}{12} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{+12}& = &6 \\\Leftrightarrow & -15x \color{red}{+12}\color{blue}{-12} & = &6\color{blue}{-12} \\\Leftrightarrow &-15x & = &-6\\\Leftrightarrow & \color{red}{-15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-4}& = &-14 \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4} & = &-14\color{blue}{+4} \\\Leftrightarrow &7x & = &-10\\\Leftrightarrow & \color{red}{7}x & = &-10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+1}& = &2 \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1} & = &2\color{blue}{-1} \\\Leftrightarrow &-6x & = &1\\\Leftrightarrow & \color{red}{-6}x & = &1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{+12}& = &15 \\\Leftrightarrow & -x \color{red}{+12}\color{blue}{-12} & = &15\color{blue}{-12} \\\Leftrightarrow &-x & = &3\\\Leftrightarrow & \color{red}{-}x & = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-9}& = &-14 \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9} & = &-14\color{blue}{+9} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+1}& = &1 \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1} & = &1\color{blue}{-1} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{-4}& = &-12 \\\Leftrightarrow & 11x \color{red}{-4}\color{blue}{+4} & = &-12\color{blue}{+4} \\\Leftrightarrow &11x & = &-8\\\Leftrightarrow & \color{red}{11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-8}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+13}& = &-12 \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13} & = &-12\color{blue}{-13} \\\Leftrightarrow &13x & = &-25\\\Leftrightarrow & \color{red}{13}x & = &-25\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-25}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{13} } & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)