Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+10}& = &-15 \\\Leftrightarrow & 10x \color{red}{+10}\color{blue}{-10} & = &-15\color{blue}{-10} \\\Leftrightarrow &10x & = &-25\\\Leftrightarrow & \color{red}{10}x & = &-25\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-25}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-8}& = &-10 \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8} & = &-10\color{blue}{+8} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-1}& = &6 \\\Leftrightarrow & -3x \color{red}{-1}\color{blue}{+1} & = &6\color{blue}{+1} \\\Leftrightarrow &-3x & = &7\\\Leftrightarrow & \color{red}{-3}x & = &7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-4}& = &-6 \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4} & = &-6\color{blue}{+4} \\\Leftrightarrow &6x & = &-2\\\Leftrightarrow & \color{red}{6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-2}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-15}& = &3 \\\Leftrightarrow & 13x \color{red}{-15}\color{blue}{+15} & = &3\color{blue}{+15} \\\Leftrightarrow &13x & = &18\\\Leftrightarrow & \color{red}{13}x & = &18\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{18}{13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{-14}& = &13 \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14} & = &13\color{blue}{+14} \\\Leftrightarrow &11x & = &27\\\Leftrightarrow & \color{red}{11}x & = &27\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{27}{11} \\\Leftrightarrow & \color{green}{ x = \frac{27}{11} } & & \\ & V = \left\{ \frac{27}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-8}& = &-8 \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8} & = &-8\color{blue}{+8} \\\Leftrightarrow &13x & = &0\\\Leftrightarrow & \color{red}{13}x & = &0\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{0}{13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+1}& = &-10 \\\Leftrightarrow & -13x \color{red}{+1}\color{blue}{-1} & = &-10\color{blue}{-1} \\\Leftrightarrow &-13x & = &-11\\\Leftrightarrow & \color{red}{-13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-1}& = &-12 \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1} & = &-12\color{blue}{+1} \\\Leftrightarrow &-13x & = &-11\\\Leftrightarrow & \color{red}{-13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+12}& = &-14 \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12} & = &-14\color{blue}{-12} \\\Leftrightarrow &8x & = &-26\\\Leftrightarrow & \color{red}{8}x & = &-26\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-26}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{4} } & & \\ & V = \left\{ \frac{-13}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-6}& = &7 \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6} & = &7\color{blue}{+6} \\\Leftrightarrow &-12x & = &13\\\Leftrightarrow & \color{red}{-12}x & = &13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{12} } & & \\ & V = \left\{ \frac{-13}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+14}& = &-8 \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14} & = &-8\color{blue}{-14} \\\Leftrightarrow &11x & = &-22\\\Leftrightarrow & \color{red}{11}x & = &-22\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-22}{11} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)