Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-1}& = &-2 \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1} & = &-2\color{blue}{+1} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+7}& = &9 \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7} & = &9\color{blue}{-7} \\\Leftrightarrow &9x & = &2\\\Leftrightarrow & \color{red}{9}x & = &2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+7}& = &8 \\\Leftrightarrow & -2x \color{red}{+7}\color{blue}{-7} & = &8\color{blue}{-7} \\\Leftrightarrow &-2x & = &1\\\Leftrightarrow & \color{red}{-2}x & = &1\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{1}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+13}& = &13 \\\Leftrightarrow & -2x \color{red}{+13}\color{blue}{-13} & = &13\color{blue}{-13} \\\Leftrightarrow &-2x & = &0\\\Leftrightarrow & \color{red}{-2}x & = &0\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{0}{-2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+9}& = &-13 \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9} & = &-13\color{blue}{-9} \\\Leftrightarrow &4x & = &-22\\\Leftrightarrow & \color{red}{4}x & = &-22\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-22}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{2} } & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+4}& = &-7 \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4} & = &-7\color{blue}{-4} \\\Leftrightarrow &-9x & = &-11\\\Leftrightarrow & \color{red}{-9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+3}& = &-11 \\\Leftrightarrow & 13x \color{red}{+3}\color{blue}{-3} & = &-11\color{blue}{-3} \\\Leftrightarrow &13x & = &-14\\\Leftrightarrow & \color{red}{13}x & = &-14\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-14}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{13} } & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-11}& = &5 \\\Leftrightarrow & -2x \color{red}{-11}\color{blue}{+11} & = &5\color{blue}{+11} \\\Leftrightarrow &-2x & = &16\\\Leftrightarrow & \color{red}{-2}x & = &16\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{16}{-2} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+3}& = &12 \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3} & = &12\color{blue}{-3} \\\Leftrightarrow &6x & = &9\\\Leftrightarrow & \color{red}{6}x & = &9\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{9}{6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{+2}& = &-2 \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2} & = &-2\color{blue}{-2} \\\Leftrightarrow &14x & = &-4\\\Leftrightarrow & \color{red}{14}x & = &-4\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-4}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-3}& = &-5 \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3} & = &-5\color{blue}{+3} \\\Leftrightarrow &-3x & = &-2\\\Leftrightarrow & \color{red}{-3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-8}& = &12 \\\Leftrightarrow & -12x \color{red}{-8}\color{blue}{+8} & = &12\color{blue}{+8} \\\Leftrightarrow &-12x & = &20\\\Leftrightarrow & \color{red}{-12}x & = &20\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{20}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)