Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+5}& = &8 \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5} & = &8\color{blue}{-5} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+9}& = &-9 \\\Leftrightarrow & 2x \color{red}{+9}\color{blue}{-9} & = &-9\color{blue}{-9} \\\Leftrightarrow &2x & = &-18\\\Leftrightarrow & \color{red}{2}x & = &-18\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-18}{2} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{+15}& = &12 \\\Leftrightarrow & -15x \color{red}{+15}\color{blue}{-15} & = &12\color{blue}{-15} \\\Leftrightarrow &-15x & = &-3\\\Leftrightarrow & \color{red}{-15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-8}& = &10 \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8} & = &10\color{blue}{+8} \\\Leftrightarrow &12x & = &18\\\Leftrightarrow & \color{red}{12}x & = &18\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{18}{12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{+2}& = &-7 \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2} & = &-7\color{blue}{-2} \\\Leftrightarrow &-11x & = &-9\\\Leftrightarrow & \color{red}{-11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-7}& = &9 \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7} & = &9\color{blue}{+7} \\\Leftrightarrow &-13x & = &16\\\Leftrightarrow & \color{red}{-13}x & = &16\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{16}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{13} } & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+2}& = &2 \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2} & = &2\color{blue}{-2} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-9}& = &-5 \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9} & = &-5\color{blue}{+9} \\\Leftrightarrow &-10x & = &4\\\Leftrightarrow & \color{red}{-10}x & = &4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-3}& = &-14 \\\Leftrightarrow & -4x \color{red}{-3}\color{blue}{+3} & = &-14\color{blue}{+3} \\\Leftrightarrow &-4x & = &-11\\\Leftrightarrow & \color{red}{-4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-11}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{+3}& = &3 \\\Leftrightarrow & 14x \color{red}{+3}\color{blue}{-3} & = &3\color{blue}{-3} \\\Leftrightarrow &14x & = &0\\\Leftrightarrow & \color{red}{14}x & = &0\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{0}{14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-2}& = &-13 \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2} & = &-13\color{blue}{+2} \\\Leftrightarrow &14x & = &-11\\\Leftrightarrow & \color{red}{14}x & = &-11\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-11}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+10}& = &7 \\\Leftrightarrow & 6x \color{red}{+10}\color{blue}{-10} & = &7\color{blue}{-10} \\\Leftrightarrow &6x & = &-3\\\Leftrightarrow & \color{red}{6}x & = &-3\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-3}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)