Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-15}& = &6 \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15} & = &6\color{blue}{+15} \\\Leftrightarrow &-2x & = &21\\\Leftrightarrow & \color{red}{-2}x & = &21\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{21}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{2} } & & \\ & V = \left\{ \frac{-21}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+14}& = &11 \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14} & = &11\color{blue}{-14} \\\Leftrightarrow &10x & = &-3\\\Leftrightarrow & \color{red}{10}x & = &-3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-9}& = &6 \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9} & = &6\color{blue}{+9} \\\Leftrightarrow &-8x & = &15\\\Leftrightarrow & \color{red}{-8}x & = &15\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{15}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{8} } & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-3}& = &12 \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3} & = &12\color{blue}{+3} \\\Leftrightarrow &6x & = &15\\\Leftrightarrow & \color{red}{6}x & = &15\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{15}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+10}& = &-6 \\\Leftrightarrow & -8x \color{red}{+10}\color{blue}{-10} & = &-6\color{blue}{-10} \\\Leftrightarrow &-8x & = &-16\\\Leftrightarrow & \color{red}{-8}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-16}{-8} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+3}& = &3 \\\Leftrightarrow & 12x \color{red}{+3}\color{blue}{-3} & = &3\color{blue}{-3} \\\Leftrightarrow &12x & = &0\\\Leftrightarrow & \color{red}{12}x & = &0\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{0}{12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{-9}& = &-9 \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9} & = &-9\color{blue}{+9} \\\Leftrightarrow &15x & = &0\\\Leftrightarrow & \color{red}{15}x & = &0\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{0}{15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-13}& = &-2 \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13} & = &-2\color{blue}{+13} \\\Leftrightarrow &12x & = &11\\\Leftrightarrow & \color{red}{12}x & = &11\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{11}{12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{12} } & & \\ & V = \left\{ \frac{11}{12} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{-1}& = &1 \\\Leftrightarrow & -9x \color{red}{-1}\color{blue}{+1} & = &1\color{blue}{+1} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-4}& = &-2 \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4} & = &-2\color{blue}{+4} \\\Leftrightarrow &8x & = &2\\\Leftrightarrow & \color{red}{8}x & = &2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+12}& = &-15 \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12} & = &-15\color{blue}{-12} \\\Leftrightarrow &5x & = &-27\\\Leftrightarrow & \color{red}{5}x & = &-27\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-27}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{5} } & & \\ & V = \left\{ \frac{-27}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{-14}& = &-14 \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14} & = &-14\color{blue}{+14} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)