Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{+14}& = &-3 \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14} & = &-3\color{blue}{-14} \\\Leftrightarrow &15x & = &-17\\\Leftrightarrow & \color{red}{15}x & = &-17\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-17}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{15} } & & \\ & V = \left\{ \frac{-17}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-6}& = &9 \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6} & = &9\color{blue}{+6} \\\Leftrightarrow &-12x & = &15\\\Leftrightarrow & \color{red}{-12}x & = &15\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{15}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-2}& = &13 \\\Leftrightarrow & 8x \color{red}{-2}\color{blue}{+2} & = &13\color{blue}{+2} \\\Leftrightarrow &8x & = &15\\\Leftrightarrow & \color{red}{8}x & = &15\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{15}{8} \\\Leftrightarrow & \color{green}{ x = \frac{15}{8} } & & \\ & V = \left\{ \frac{15}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-11}& = &3 \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11} & = &3\color{blue}{+11} \\\Leftrightarrow &15x & = &14\\\Leftrightarrow & \color{red}{15}x & = &14\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{14}{15} \\\Leftrightarrow & \color{green}{ x = \frac{14}{15} } & & \\ & V = \left\{ \frac{14}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-12}& = &7 \\\Leftrightarrow & 10x \color{red}{-12}\color{blue}{+12} & = &7\color{blue}{+12} \\\Leftrightarrow &10x & = &19\\\Leftrightarrow & \color{red}{10}x & = &19\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{19}{10} \\\Leftrightarrow & \color{green}{ x = \frac{19}{10} } & & \\ & V = \left\{ \frac{19}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-11}& = &-1 \\\Leftrightarrow & 6x \color{red}{-11}\color{blue}{+11} & = &-1\color{blue}{+11} \\\Leftrightarrow &6x & = &10\\\Leftrightarrow & \color{red}{6}x & = &10\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{10}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+11}& = &-8 \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11} & = &-8\color{blue}{-11} \\\Leftrightarrow &-13x & = &-19\\\Leftrightarrow & \color{red}{-13}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{19}{13} } & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{+7}& = &-13 \\\Leftrightarrow & -4x \color{red}{+7}\color{blue}{-7} & = &-13\color{blue}{-7} \\\Leftrightarrow &-4x & = &-20\\\Leftrightarrow & \color{red}{-4}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-20}{-4} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-13}& = &6 \\\Leftrightarrow & 13x \color{red}{-13}\color{blue}{+13} & = &6\color{blue}{+13} \\\Leftrightarrow &13x & = &19\\\Leftrightarrow & \color{red}{13}x & = &19\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{19}{13} \\\Leftrightarrow & \color{green}{ x = \frac{19}{13} } & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-10}& = &-13 \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10} & = &-13\color{blue}{+10} \\\Leftrightarrow &10x & = &-3\\\Leftrightarrow & \color{red}{10}x & = &-3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+12}& = &6 \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12} & = &6\color{blue}{-12} \\\Leftrightarrow &-14x & = &-6\\\Leftrightarrow & \color{red}{-14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{+1}& = &2 \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1} & = &2\color{blue}{-1} \\\Leftrightarrow &12x & = &1\\\Leftrightarrow & \color{red}{12}x & = &1\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{1}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)