Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-3}& = &-5 \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3} & = &-5\color{blue}{+3} \\\Leftrightarrow &6x & = &-2\\\Leftrightarrow & \color{red}{6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-2}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-4}& = &-5 \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4} & = &-5\color{blue}{+4} \\\Leftrightarrow &-10x & = &-1\\\Leftrightarrow & \color{red}{-10}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-5}& = &2 \\\Leftrightarrow & 12x \color{red}{-5}\color{blue}{+5} & = &2\color{blue}{+5} \\\Leftrightarrow &12x & = &7\\\Leftrightarrow & \color{red}{12}x & = &7\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{7}{12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+7}& = &-15 \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7} & = &-15\color{blue}{-7} \\\Leftrightarrow &15x & = &-22\\\Leftrightarrow & \color{red}{15}x & = &-22\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-22}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{15} } & & \\ & V = \left\{ \frac{-22}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-15}& = &-2 \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15} & = &-2\color{blue}{+15} \\\Leftrightarrow &-12x & = &13\\\Leftrightarrow & \color{red}{-12}x & = &13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{12} } & & \\ & V = \left\{ \frac{-13}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-8}& = &-2 \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8} & = &-2\color{blue}{+8} \\\Leftrightarrow &-9x & = &6\\\Leftrightarrow & \color{red}{-9}x & = &6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{-4}& = &5 \\\Leftrightarrow & 10x \color{red}{-4}\color{blue}{+4} & = &5\color{blue}{+4} \\\Leftrightarrow &10x & = &9\\\Leftrightarrow & \color{red}{10}x & = &9\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{9}{10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+14}& = &2 \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14} & = &2\color{blue}{-14} \\\Leftrightarrow &10x & = &-12\\\Leftrightarrow & \color{red}{10}x & = &-12\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-12}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{+13}& = &-12 \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13} & = &-12\color{blue}{-13} \\\Leftrightarrow &3x & = &-25\\\Leftrightarrow & \color{red}{3}x & = &-25\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-25}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{3} } & & \\ & V = \left\{ \frac{-25}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+9}& = &-6 \\\Leftrightarrow & 2x \color{red}{+9}\color{blue}{-9} & = &-6\color{blue}{-9} \\\Leftrightarrow &2x & = &-15\\\Leftrightarrow & \color{red}{2}x & = &-15\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-15}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{2} } & & \\ & V = \left\{ \frac{-15}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-6}& = &-4 \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6} & = &-4\color{blue}{+6} \\\Leftrightarrow &4x & = &2\\\Leftrightarrow & \color{red}{4}x & = &2\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{2}{4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+13}& = &-3 \\\Leftrightarrow & -2x \color{red}{+13}\color{blue}{-13} & = &-3\color{blue}{-13} \\\Leftrightarrow &-2x & = &-16\\\Leftrightarrow & \color{red}{-2}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-16}{-2} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)