Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-1}& = &11 \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1} & = &11\color{blue}{+1} \\\Leftrightarrow &14x & = &12\\\Leftrightarrow & \color{red}{14}x & = &12\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{12}{14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{-10}& = &-2 \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10} & = &-2\color{blue}{+10} \\\Leftrightarrow &2x & = &8\\\Leftrightarrow & \color{red}{2}x & = &8\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{8}{2} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-3}& = &-14 \\\Leftrightarrow & -2x \color{red}{-3}\color{blue}{+3} & = &-14\color{blue}{+3} \\\Leftrightarrow &-2x & = &-11\\\Leftrightarrow & \color{red}{-2}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-11}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-10}& = &7 \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10} & = &7\color{blue}{+10} \\\Leftrightarrow &2x & = &17\\\Leftrightarrow & \color{red}{2}x & = &17\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{17}{2} \\\Leftrightarrow & \color{green}{ x = \frac{17}{2} } & & \\ & V = \left\{ \frac{17}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{-6}& = &-9 \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6} & = &-9\color{blue}{+6} \\\Leftrightarrow &7x & = &-3\\\Leftrightarrow & \color{red}{7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+8}& = &4 \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8} & = &4\color{blue}{-8} \\\Leftrightarrow &9x & = &-4\\\Leftrightarrow & \color{red}{9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-6}& = &-3 \\\Leftrightarrow & -8x \color{red}{-6}\color{blue}{+6} & = &-3\color{blue}{+6} \\\Leftrightarrow &-8x & = &3\\\Leftrightarrow & \color{red}{-8}x & = &3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-7}& = &5 \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7} & = &5\color{blue}{+7} \\\Leftrightarrow &13x & = &12\\\Leftrightarrow & \color{red}{13}x & = &12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-8}& = &-3 \\\Leftrightarrow & 6x \color{red}{-8}\color{blue}{+8} & = &-3\color{blue}{+8} \\\Leftrightarrow &6x & = &5\\\Leftrightarrow & \color{red}{6}x & = &5\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{5}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-1}& = &-15 \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1} & = &-15\color{blue}{+1} \\\Leftrightarrow &-x & = &-14\\\Leftrightarrow & \color{red}{-}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-14}{-1} \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-14}& = &-12 \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14} & = &-12\color{blue}{+14} \\\Leftrightarrow &-2x & = &2\\\Leftrightarrow & \color{red}{-2}x & = &2\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{2}{-2} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+3}& = &5 \\\Leftrightarrow & 14x \color{red}{+3}\color{blue}{-3} & = &5\color{blue}{-3} \\\Leftrightarrow &14x & = &2\\\Leftrightarrow & \color{red}{14}x & = &2\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{2}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)