Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-4}& = &-2 \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4} & = &-2\color{blue}{+4} \\\Leftrightarrow &13x & = &2\\\Leftrightarrow & \color{red}{13}x & = &2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-15}& = &9 \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15} & = &9\color{blue}{+15} \\\Leftrightarrow &-12x & = &24\\\Leftrightarrow & \color{red}{-12}x & = &24\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{24}{-12} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+14}& = &4 \\\Leftrightarrow & 8x \color{red}{+14}\color{blue}{-14} & = &4\color{blue}{-14} \\\Leftrightarrow &8x & = &-10\\\Leftrightarrow & \color{red}{8}x & = &-10\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-10}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+4}& = &10 \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4} & = &10\color{blue}{-4} \\\Leftrightarrow &-7x & = &6\\\Leftrightarrow & \color{red}{-7}x & = &6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{+8}& = &-5 \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8} & = &-5\color{blue}{-8} \\\Leftrightarrow &2x & = &-13\\\Leftrightarrow & \color{red}{2}x & = &-13\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-13}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{2} } & & \\ & V = \left\{ \frac{-13}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{+6}& = &4 \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6} & = &4\color{blue}{-6} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{-1}& = &1 \\\Leftrightarrow & -7x \color{red}{-1}\color{blue}{+1} & = &1\color{blue}{+1} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{-6}& = &4 \\\Leftrightarrow & 2x \color{red}{-6}\color{blue}{+6} & = &4\color{blue}{+6} \\\Leftrightarrow &2x & = &10\\\Leftrightarrow & \color{red}{2}x & = &10\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{10}{2} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{-1}& = &7 \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1} & = &7\color{blue}{+1} \\\Leftrightarrow &-x & = &8\\\Leftrightarrow & \color{red}{-}x & = &8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{8}{-1} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-3}& = &7 \\\Leftrightarrow & -14x \color{red}{-3}\color{blue}{+3} & = &7\color{blue}{+3} \\\Leftrightarrow &-14x & = &10\\\Leftrightarrow & \color{red}{-14}x & = &10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-3}& = &-15 \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3} & = &-15\color{blue}{+3} \\\Leftrightarrow &7x & = &-12\\\Leftrightarrow & \color{red}{7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-12}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+7}& = &8 \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7} & = &8\color{blue}{-7} \\\Leftrightarrow &5x & = &1\\\Leftrightarrow & \color{red}{5}x & = &1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)