Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+1}& = &14 \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1} & = &14\color{blue}{-1} \\\Leftrightarrow &-8x & = &13\\\Leftrightarrow & \color{red}{-8}x & = &13\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{13}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{8} } & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{-10}& = &14 \\\Leftrightarrow & 13x \color{red}{-10}\color{blue}{+10} & = &14\color{blue}{+10} \\\Leftrightarrow &13x & = &24\\\Leftrightarrow & \color{red}{13}x & = &24\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{24}{13} \\\Leftrightarrow & \color{green}{ x = \frac{24}{13} } & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-10}& = &13 \\\Leftrightarrow & -8x \color{red}{-10}\color{blue}{+10} & = &13\color{blue}{+10} \\\Leftrightarrow &-8x & = &23\\\Leftrightarrow & \color{red}{-8}x & = &23\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{23}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{8} } & & \\ & V = \left\{ \frac{-23}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+7}& = &-12 \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7} & = &-12\color{blue}{-7} \\\Leftrightarrow &-10x & = &-19\\\Leftrightarrow & \color{red}{-10}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-19}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{19}{10} } & & \\ & V = \left\{ \frac{19}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+14}& = &-4 \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14} & = &-4\color{blue}{-14} \\\Leftrightarrow &-13x & = &-18\\\Leftrightarrow & \color{red}{-13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-18}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+6}& = &10 \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6} & = &10\color{blue}{-6} \\\Leftrightarrow &9x & = &4\\\Leftrightarrow & \color{red}{9}x & = &4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{+14}& = &-2 \\\Leftrightarrow & -11x \color{red}{+14}\color{blue}{-14} & = &-2\color{blue}{-14} \\\Leftrightarrow &-11x & = &-16\\\Leftrightarrow & \color{red}{-11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+14}& = &9 \\\Leftrightarrow & -15x \color{red}{+14}\color{blue}{-14} & = &9\color{blue}{-14} \\\Leftrightarrow &-15x & = &-5\\\Leftrightarrow & \color{red}{-15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-3}& = &-8 \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3} & = &-8\color{blue}{+3} \\\Leftrightarrow &-6x & = &-5\\\Leftrightarrow & \color{red}{-6}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-4}& = &9 \\\Leftrightarrow & 11x \color{red}{-4}\color{blue}{+4} & = &9\color{blue}{+4} \\\Leftrightarrow &11x & = &13\\\Leftrightarrow & \color{red}{11}x & = &13\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{13}{11} \\\Leftrightarrow & \color{green}{ x = \frac{13}{11} } & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+3}& = &9 \\\Leftrightarrow & 13x \color{red}{+3}\color{blue}{-3} & = &9\color{blue}{-3} \\\Leftrightarrow &13x & = &6\\\Leftrightarrow & \color{red}{13}x & = &6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+10}& = &-4 \\\Leftrightarrow & 4x \color{red}{+10}\color{blue}{-10} & = &-4\color{blue}{-10} \\\Leftrightarrow &4x & = &-14\\\Leftrightarrow & \color{red}{4}x & = &-14\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-14}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)