Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-10}& = &-12 \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10} & = &-12\color{blue}{+10} \\\Leftrightarrow &-2x & = &-2\\\Leftrightarrow & \color{red}{-2}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-2}{-2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-15}& = &12 \\\Leftrightarrow & 4x \color{red}{-15}\color{blue}{+15} & = &12\color{blue}{+15} \\\Leftrightarrow &4x & = &27\\\Leftrightarrow & \color{red}{4}x & = &27\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{27}{4} \\\Leftrightarrow & \color{green}{ x = \frac{27}{4} } & & \\ & V = \left\{ \frac{27}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-12}& = &3 \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12} & = &3\color{blue}{+12} \\\Leftrightarrow &-2x & = &15\\\Leftrightarrow & \color{red}{-2}x & = &15\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{15}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{2} } & & \\ & V = \left\{ \frac{-15}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+5}& = &8 \\\Leftrightarrow & -4x \color{red}{+5}\color{blue}{-5} & = &8\color{blue}{-5} \\\Leftrightarrow &-4x & = &3\\\Leftrightarrow & \color{red}{-4}x & = &3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-3}& = &8 \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3} & = &8\color{blue}{+3} \\\Leftrightarrow &-5x & = &11\\\Leftrightarrow & \color{red}{-5}x & = &11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+4}& = &-3 \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4} & = &-3\color{blue}{-4} \\\Leftrightarrow &-10x & = &-7\\\Leftrightarrow & \color{red}{-10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-5}& = &-8 \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5} & = &-8\color{blue}{+5} \\\Leftrightarrow &-5x & = &-3\\\Leftrightarrow & \color{red}{-5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-8}& = &7 \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8} & = &7\color{blue}{+8} \\\Leftrightarrow &-11x & = &15\\\Leftrightarrow & \color{red}{-11}x & = &15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{11} } & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{+2}& = &-5 \\\Leftrightarrow & 3x \color{red}{+2}\color{blue}{-2} & = &-5\color{blue}{-2} \\\Leftrightarrow &3x & = &-7\\\Leftrightarrow & \color{red}{3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-7}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-11}& = &5 \\\Leftrightarrow & 10x \color{red}{-11}\color{blue}{+11} & = &5\color{blue}{+11} \\\Leftrightarrow &10x & = &16\\\Leftrightarrow & \color{red}{10}x & = &16\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{16}{10} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-7}& = &3 \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7} & = &3\color{blue}{+7} \\\Leftrightarrow &13x & = &10\\\Leftrightarrow & \color{red}{13}x & = &10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-12}& = &9 \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12} & = &9\color{blue}{+12} \\\Leftrightarrow &6x & = &21\\\Leftrightarrow & \color{red}{6}x & = &21\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{21}{6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)