Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+5}& = &-9 \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5} & = &-9\color{blue}{-5} \\\Leftrightarrow &-3x & = &-14\\\Leftrightarrow & \color{red}{-3}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-14}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{14}{3} } & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+12}& = &7 \\\Leftrightarrow & -6x \color{red}{+12}\color{blue}{-12} & = &7\color{blue}{-12} \\\Leftrightarrow &-6x & = &-5\\\Leftrightarrow & \color{red}{-6}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-15}& = &-13 \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15} & = &-13\color{blue}{+15} \\\Leftrightarrow &-13x & = &2\\\Leftrightarrow & \color{red}{-13}x & = &2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{+14}& = &2 \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14} & = &2\color{blue}{-14} \\\Leftrightarrow &-8x & = &-12\\\Leftrightarrow & \color{red}{-8}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-12}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{-11}& = &15 \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11} & = &15\color{blue}{+11} \\\Leftrightarrow &-6x & = &26\\\Leftrightarrow & \color{red}{-6}x & = &26\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{26}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+15}& = &8 \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15} & = &8\color{blue}{-15} \\\Leftrightarrow &11x & = &-7\\\Leftrightarrow & \color{red}{11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+8}& = &7 \\\Leftrightarrow & -x \color{red}{+8}\color{blue}{-8} & = &7\color{blue}{-8} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-8}& = &-9 \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8} & = &-9\color{blue}{+8} \\\Leftrightarrow &10x & = &-1\\\Leftrightarrow & \color{red}{10}x & = &-1\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-1}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+11}& = &-8 \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11} & = &-8\color{blue}{-11} \\\Leftrightarrow &-6x & = &-19\\\Leftrightarrow & \color{red}{-6}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-19}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{19}{6} } & & \\ & V = \left\{ \frac{19}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-5}& = &-2 \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5} & = &-2\color{blue}{+5} \\\Leftrightarrow &-8x & = &3\\\Leftrightarrow & \color{red}{-8}x & = &3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-4}& = &9 \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4} & = &9\color{blue}{+4} \\\Leftrightarrow &4x & = &13\\\Leftrightarrow & \color{red}{4}x & = &13\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{13}{4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-5}& = &11 \\\Leftrightarrow & 11x \color{red}{-5}\color{blue}{+5} & = &11\color{blue}{+5} \\\Leftrightarrow &11x & = &16\\\Leftrightarrow & \color{red}{11}x & = &16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)