Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+14}& = &6 \\\Leftrightarrow & -14x \color{red}{+14}\color{blue}{-14} & = &6\color{blue}{-14} \\\Leftrightarrow &-14x & = &-8\\\Leftrightarrow & \color{red}{-14}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+3}& = &-15 \\\Leftrightarrow & -2x \color{red}{+3}\color{blue}{-3} & = &-15\color{blue}{-3} \\\Leftrightarrow &-2x & = &-18\\\Leftrightarrow & \color{red}{-2}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-18}{-2} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+1}& = &11 \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1} & = &11\color{blue}{-1} \\\Leftrightarrow &-12x & = &10\\\Leftrightarrow & \color{red}{-12}x & = &10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{-11}& = &-5 \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11} & = &-5\color{blue}{+11} \\\Leftrightarrow &-8x & = &6\\\Leftrightarrow & \color{red}{-8}x & = &6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+14}& = &4 \\\Leftrightarrow & 7x \color{red}{+14}\color{blue}{-14} & = &4\color{blue}{-14} \\\Leftrightarrow &7x & = &-10\\\Leftrightarrow & \color{red}{7}x & = &-10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-15}& = &4 \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15} & = &4\color{blue}{+15} \\\Leftrightarrow &-5x & = &19\\\Leftrightarrow & \color{red}{-5}x & = &19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{5} } & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+8}& = &-5 \\\Leftrightarrow & 13x \color{red}{+8}\color{blue}{-8} & = &-5\color{blue}{-8} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-15}& = &14 \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15} & = &14\color{blue}{+15} \\\Leftrightarrow &7x & = &29\\\Leftrightarrow & \color{red}{7}x & = &29\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{29}{7} \\\Leftrightarrow & \color{green}{ x = \frac{29}{7} } & & \\ & V = \left\{ \frac{29}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+13}& = &-1 \\\Leftrightarrow & 12x \color{red}{+13}\color{blue}{-13} & = &-1\color{blue}{-13} \\\Leftrightarrow &12x & = &-14\\\Leftrightarrow & \color{red}{12}x & = &-14\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-14}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+15}& = &9 \\\Leftrightarrow & -15x \color{red}{+15}\color{blue}{-15} & = &9\color{blue}{-15} \\\Leftrightarrow &-15x & = &-6\\\Leftrightarrow & \color{red}{-15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+6}& = &3 \\\Leftrightarrow & -3x \color{red}{+6}\color{blue}{-6} & = &3\color{blue}{-6} \\\Leftrightarrow &-3x & = &-3\\\Leftrightarrow & \color{red}{-3}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-3}{-3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-8}& = &-4 \\\Leftrightarrow & -3x \color{red}{-8}\color{blue}{+8} & = &-4\color{blue}{+8} \\\Leftrightarrow &-3x & = &4\\\Leftrightarrow & \color{red}{-3}x & = &4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)