Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-5}& = &-11 \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5} & = &-11\color{blue}{+5} \\\Leftrightarrow &4x & = &-6\\\Leftrightarrow & \color{red}{4}x & = &-6\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-6}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-2}& = &-14 \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2} & = &-14\color{blue}{+2} \\\Leftrightarrow &6x & = &-12\\\Leftrightarrow & \color{red}{6}x & = &-12\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-12}{6} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-6}& = &4 \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6} & = &4\color{blue}{+6} \\\Leftrightarrow &5x & = &10\\\Leftrightarrow & \color{red}{5}x & = &10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{10}{5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+2}& = &5 \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2} & = &5\color{blue}{-2} \\\Leftrightarrow &-6x & = &3\\\Leftrightarrow & \color{red}{-6}x & = &3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+5}& = &4 \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5} & = &4\color{blue}{-5} \\\Leftrightarrow &6x & = &-1\\\Leftrightarrow & \color{red}{6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-1}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+13}& = &-9 \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13} & = &-9\color{blue}{-13} \\\Leftrightarrow &8x & = &-22\\\Leftrightarrow & \color{red}{8}x & = &-22\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-22}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{-5}& = &9 \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5} & = &9\color{blue}{+5} \\\Leftrightarrow &6x & = &14\\\Leftrightarrow & \color{red}{6}x & = &14\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{14}{6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-11}& = &-2 \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11} & = &-2\color{blue}{+11} \\\Leftrightarrow &7x & = &9\\\Leftrightarrow & \color{red}{7}x & = &9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-4}& = &-13 \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4} & = &-13\color{blue}{+4} \\\Leftrightarrow &-10x & = &-9\\\Leftrightarrow & \color{red}{-10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-8}& = &-4 \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8} & = &-4\color{blue}{+8} \\\Leftrightarrow &-8x & = &4\\\Leftrightarrow & \color{red}{-8}x & = &4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-3}& = &-2 \\\Leftrightarrow & -14x \color{red}{-3}\color{blue}{+3} & = &-2\color{blue}{+3} \\\Leftrightarrow &-14x & = &1\\\Leftrightarrow & \color{red}{-14}x & = &1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+4}& = &-14 \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4} & = &-14\color{blue}{-4} \\\Leftrightarrow &-7x & = &-18\\\Leftrightarrow & \color{red}{-7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{18}{7} } & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)