Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{-15}& = &13 \\\Leftrightarrow & -8x \color{red}{-15}\color{blue}{+15} & = &13\color{blue}{+15} \\\Leftrightarrow &-8x & = &28\\\Leftrightarrow & \color{red}{-8}x & = &28\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{28}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+5}& = &2 \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5} & = &2\color{blue}{-5} \\\Leftrightarrow &6x & = &-3\\\Leftrightarrow & \color{red}{6}x & = &-3\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-3}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{+14}& = &7 \\\Leftrightarrow & -x \color{red}{+14}\color{blue}{-14} & = &7\color{blue}{-14} \\\Leftrightarrow &-x & = &-7\\\Leftrightarrow & \color{red}{-}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-7}{-1} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-13}& = &-6 \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13} & = &-6\color{blue}{+13} \\\Leftrightarrow &3x & = &7\\\Leftrightarrow & \color{red}{3}x & = &7\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{7}{3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-10}& = &-2 \\\Leftrightarrow & 13x \color{red}{-10}\color{blue}{+10} & = &-2\color{blue}{+10} \\\Leftrightarrow &13x & = &8\\\Leftrightarrow & \color{red}{13}x & = &8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+13}& = &-1 \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13} & = &-1\color{blue}{-13} \\\Leftrightarrow &13x & = &-14\\\Leftrightarrow & \color{red}{13}x & = &-14\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-14}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{13} } & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+9}& = &9 \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9} & = &9\color{blue}{-9} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-12}& = &-15 \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12} & = &-15\color{blue}{+12} \\\Leftrightarrow &-8x & = &-3\\\Leftrightarrow & \color{red}{-8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+8}& = &-3 \\\Leftrightarrow & -x \color{red}{+8}\color{blue}{-8} & = &-3\color{blue}{-8} \\\Leftrightarrow &-x & = &-11\\\Leftrightarrow & \color{red}{-}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-11}{-1} \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+5}& = &-13 \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5} & = &-13\color{blue}{-5} \\\Leftrightarrow &8x & = &-18\\\Leftrightarrow & \color{red}{8}x & = &-18\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-18}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+5}& = &-3 \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5} & = &-3\color{blue}{-5} \\\Leftrightarrow &6x & = &-8\\\Leftrightarrow & \color{red}{6}x & = &-8\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-8}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-9}& = &14 \\\Leftrightarrow & 13x \color{red}{-9}\color{blue}{+9} & = &14\color{blue}{+9} \\\Leftrightarrow &13x & = &23\\\Leftrightarrow & \color{red}{13}x & = &23\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{23}{13} \\\Leftrightarrow & \color{green}{ x = \frac{23}{13} } & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)