Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+5}& = &8 \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5} & = &8\color{blue}{-5} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{-10}& = &-3 \\\Leftrightarrow & 9x \color{red}{-10}\color{blue}{+10} & = &-3\color{blue}{+10} \\\Leftrightarrow &9x & = &7\\\Leftrightarrow & \color{red}{9}x & = &7\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{7}{9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+10}& = &-9 \\\Leftrightarrow & -8x \color{red}{+10}\color{blue}{-10} & = &-9\color{blue}{-10} \\\Leftrightarrow &-8x & = &-19\\\Leftrightarrow & \color{red}{-8}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-19}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{19}{8} } & & \\ & V = \left\{ \frac{19}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+15}& = &-1 \\\Leftrightarrow & 3x \color{red}{+15}\color{blue}{-15} & = &-1\color{blue}{-15} \\\Leftrightarrow &3x & = &-16\\\Leftrightarrow & \color{red}{3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-16}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-1}& = &3 \\\Leftrightarrow & -2x \color{red}{-1}\color{blue}{+1} & = &3\color{blue}{+1} \\\Leftrightarrow &-2x & = &4\\\Leftrightarrow & \color{red}{-2}x & = &4\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{4}{-2} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-7}& = &6 \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7} & = &6\color{blue}{+7} \\\Leftrightarrow &-2x & = &13\\\Leftrightarrow & \color{red}{-2}x & = &13\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{13}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{2} } & & \\ & V = \left\{ \frac{-13}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{-11}& = &15 \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11} & = &15\color{blue}{+11} \\\Leftrightarrow &-14x & = &26\\\Leftrightarrow & \color{red}{-14}x & = &26\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{26}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-14}& = &9 \\\Leftrightarrow & -15x \color{red}{-14}\color{blue}{+14} & = &9\color{blue}{+14} \\\Leftrightarrow &-15x & = &23\\\Leftrightarrow & \color{red}{-15}x & = &23\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{23}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{15} } & & \\ & V = \left\{ \frac{-23}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-1}& = &1 \\\Leftrightarrow & 11x \color{red}{-1}\color{blue}{+1} & = &1\color{blue}{+1} \\\Leftrightarrow &11x & = &2\\\Leftrightarrow & \color{red}{11}x & = &2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+1}& = &1 \\\Leftrightarrow & 10x \color{red}{+1}\color{blue}{-1} & = &1\color{blue}{-1} \\\Leftrightarrow &10x & = &0\\\Leftrightarrow & \color{red}{10}x & = &0\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{0}{10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-5}& = &-7 \\\Leftrightarrow & 13x \color{red}{-5}\color{blue}{+5} & = &-7\color{blue}{+5} \\\Leftrightarrow &13x & = &-2\\\Leftrightarrow & \color{red}{13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-8}& = &-9 \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8} & = &-9\color{blue}{+8} \\\Leftrightarrow &15x & = &-1\\\Leftrightarrow & \color{red}{15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-1}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)