Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{-5}& = &7 \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5} & = &7\color{blue}{+5} \\\Leftrightarrow &-8x & = &12\\\Leftrightarrow & \color{red}{-8}x & = &12\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{12}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{+5}& = &3 \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5} & = &3\color{blue}{-5} \\\Leftrightarrow &-14x & = &-2\\\Leftrightarrow & \color{red}{-14}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-11}& = &7 \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11} & = &7\color{blue}{+11} \\\Leftrightarrow &9x & = &18\\\Leftrightarrow & \color{red}{9}x & = &18\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{18}{9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-14}& = &14 \\\Leftrightarrow & 7x \color{red}{-14}\color{blue}{+14} & = &14\color{blue}{+14} \\\Leftrightarrow &7x & = &28\\\Leftrightarrow & \color{red}{7}x & = &28\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{28}{7} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{-7}& = &5 \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7} & = &5\color{blue}{+7} \\\Leftrightarrow &5x & = &12\\\Leftrightarrow & \color{red}{5}x & = &12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+7}& = &7 \\\Leftrightarrow & 3x \color{red}{+7}\color{blue}{-7} & = &7\color{blue}{-7} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-10}& = &11 \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10} & = &11\color{blue}{+10} \\\Leftrightarrow &7x & = &21\\\Leftrightarrow & \color{red}{7}x & = &21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{21}{7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-4}& = &-8 \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4} & = &-8\color{blue}{+4} \\\Leftrightarrow &13x & = &-4\\\Leftrightarrow & \color{red}{13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-1}& = &14 \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1} & = &14\color{blue}{+1} \\\Leftrightarrow &12x & = &15\\\Leftrightarrow & \color{red}{12}x & = &15\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{15}{12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-1}& = &-2 \\\Leftrightarrow & -4x \color{red}{-1}\color{blue}{+1} & = &-2\color{blue}{+1} \\\Leftrightarrow &-4x & = &-1\\\Leftrightarrow & \color{red}{-4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+8}& = &-8 \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8} & = &-8\color{blue}{-8} \\\Leftrightarrow &6x & = &-16\\\Leftrightarrow & \color{red}{6}x & = &-16\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-16}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{+12}& = &-2 \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12} & = &-2\color{blue}{-12} \\\Leftrightarrow &12x & = &-14\\\Leftrightarrow & \color{red}{12}x & = &-14\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-14}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)