Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-12}& = &-6 \\\Leftrightarrow & 10x \color{red}{-12}\color{blue}{+12} & = &-6\color{blue}{+12} \\\Leftrightarrow &10x & = &6\\\Leftrightarrow & \color{red}{10}x & = &6\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{6}{10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{-1}& = &-13 \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1} & = &-13\color{blue}{+1} \\\Leftrightarrow &-5x & = &-12\\\Leftrightarrow & \color{red}{-5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+15}& = &12 \\\Leftrightarrow & -2x \color{red}{+15}\color{blue}{-15} & = &12\color{blue}{-15} \\\Leftrightarrow &-2x & = &-3\\\Leftrightarrow & \color{red}{-2}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-3}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+11}& = &8 \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11} & = &8\color{blue}{-11} \\\Leftrightarrow &12x & = &-3\\\Leftrightarrow & \color{red}{12}x & = &-3\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-3}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+8}& = &-6 \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8} & = &-6\color{blue}{-8} \\\Leftrightarrow &-14x & = &-14\\\Leftrightarrow & \color{red}{-14}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-14}{-14} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{-2}& = &13 \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2} & = &13\color{blue}{+2} \\\Leftrightarrow &11x & = &15\\\Leftrightarrow & \color{red}{11}x & = &15\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{15}{11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{-13}& = &4 \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13} & = &4\color{blue}{+13} \\\Leftrightarrow &6x & = &17\\\Leftrightarrow & \color{red}{6}x & = &17\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{17}{6} \\\Leftrightarrow & \color{green}{ x = \frac{17}{6} } & & \\ & V = \left\{ \frac{17}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-15}& = &3 \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15} & = &3\color{blue}{+15} \\\Leftrightarrow &-4x & = &18\\\Leftrightarrow & \color{red}{-4}x & = &18\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{18}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-14}& = &11 \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14} & = &11\color{blue}{+14} \\\Leftrightarrow &13x & = &25\\\Leftrightarrow & \color{red}{13}x & = &25\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{25}{13} \\\Leftrightarrow & \color{green}{ x = \frac{25}{13} } & & \\ & V = \left\{ \frac{25}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+6}& = &13 \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6} & = &13\color{blue}{-6} \\\Leftrightarrow &3x & = &7\\\Leftrightarrow & \color{red}{3}x & = &7\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{7}{3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+4}& = &-14 \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4} & = &-14\color{blue}{-4} \\\Leftrightarrow &6x & = &-18\\\Leftrightarrow & \color{red}{6}x & = &-18\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-18}{6} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+6}& = &-15 \\\Leftrightarrow & -13x \color{red}{+6}\color{blue}{-6} & = &-15\color{blue}{-6} \\\Leftrightarrow &-13x & = &-21\\\Leftrightarrow & \color{red}{-13}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-21}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{21}{13} } & & \\ & V = \left\{ \frac{21}{13} \right\} & \\\end{align}\)