Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-8}& = &-11 \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8} & = &-11\color{blue}{+8} \\\Leftrightarrow &4x & = &-3\\\Leftrightarrow & \color{red}{4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{-14}& = &-11 \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14} & = &-11\color{blue}{+14} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+13}& = &14 \\\Leftrightarrow & 14x \color{red}{+13}\color{blue}{-13} & = &14\color{blue}{-13} \\\Leftrightarrow &14x & = &1\\\Leftrightarrow & \color{red}{14}x & = &1\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{1}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-9}& = &-3 \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9} & = &-3\color{blue}{+9} \\\Leftrightarrow &12x & = &6\\\Leftrightarrow & \color{red}{12}x & = &6\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{6}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{-1}& = &-13 \\\Leftrightarrow & -9x \color{red}{-1}\color{blue}{+1} & = &-13\color{blue}{+1} \\\Leftrightarrow &-9x & = &-12\\\Leftrightarrow & \color{red}{-9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{-12}& = &-10 \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12} & = &-10\color{blue}{+12} \\\Leftrightarrow &3x & = &2\\\Leftrightarrow & \color{red}{3}x & = &2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+5}& = &-6 \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5} & = &-6\color{blue}{-5} \\\Leftrightarrow &13x & = &-11\\\Leftrightarrow & \color{red}{13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{+2}& = &10 \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2} & = &10\color{blue}{-2} \\\Leftrightarrow &-x & = &8\\\Leftrightarrow & \color{red}{-}x & = &8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{8}{-1} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-5}& = &-10 \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5} & = &-10\color{blue}{+5} \\\Leftrightarrow &-2x & = &-5\\\Leftrightarrow & \color{red}{-2}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-5}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+1}& = &-15 \\\Leftrightarrow & 10x \color{red}{+1}\color{blue}{-1} & = &-15\color{blue}{-1} \\\Leftrightarrow &10x & = &-16\\\Leftrightarrow & \color{red}{10}x & = &-16\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-16}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+5}& = &13 \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5} & = &13\color{blue}{-5} \\\Leftrightarrow &-13x & = &8\\\Leftrightarrow & \color{red}{-13}x & = &8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-5}& = &13 \\\Leftrightarrow & -10x \color{red}{-5}\color{blue}{+5} & = &13\color{blue}{+5} \\\Leftrightarrow &-10x & = &18\\\Leftrightarrow & \color{red}{-10}x & = &18\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{18}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)