Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+3}& = &14 \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3} & = &14\color{blue}{-3} \\\Leftrightarrow &3x & = &11\\\Leftrightarrow & \color{red}{3}x & = &11\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{11}{3} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+5}& = &6 \\\Leftrightarrow & 2x \color{red}{+5}\color{blue}{-5} & = &6\color{blue}{-5} \\\Leftrightarrow &2x & = &1\\\Leftrightarrow & \color{red}{2}x & = &1\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{1}{2} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-12}& = &11 \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12} & = &11\color{blue}{+12} \\\Leftrightarrow &7x & = &23\\\Leftrightarrow & \color{red}{7}x & = &23\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{23}{7} \\\Leftrightarrow & \color{green}{ x = \frac{23}{7} } & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-12}& = &-7 \\\Leftrightarrow & -14x \color{red}{-12}\color{blue}{+12} & = &-7\color{blue}{+12} \\\Leftrightarrow &-14x & = &5\\\Leftrightarrow & \color{red}{-14}x & = &5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{14} } & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{-4}& = &5 \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4} & = &5\color{blue}{+4} \\\Leftrightarrow &-10x & = &9\\\Leftrightarrow & \color{red}{-10}x & = &9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+4}& = &-13 \\\Leftrightarrow & 10x \color{red}{+4}\color{blue}{-4} & = &-13\color{blue}{-4} \\\Leftrightarrow &10x & = &-17\\\Leftrightarrow & \color{red}{10}x & = &-17\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-17}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{10} } & & \\ & V = \left\{ \frac{-17}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{+10}& = &-14 \\\Leftrightarrow & 6x \color{red}{+10}\color{blue}{-10} & = &-14\color{blue}{-10} \\\Leftrightarrow &6x & = &-24\\\Leftrightarrow & \color{red}{6}x & = &-24\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-24}{6} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-13}& = &-2 \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13} & = &-2\color{blue}{+13} \\\Leftrightarrow &10x & = &11\\\Leftrightarrow & \color{red}{10}x & = &11\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{11}{10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{10} } & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-14}& = &13 \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14} & = &13\color{blue}{+14} \\\Leftrightarrow &-2x & = &27\\\Leftrightarrow & \color{red}{-2}x & = &27\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{27}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{2} } & & \\ & V = \left\{ \frac{-27}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+2}& = &-13 \\\Leftrightarrow & 7x \color{red}{+2}\color{blue}{-2} & = &-13\color{blue}{-2} \\\Leftrightarrow &7x & = &-15\\\Leftrightarrow & \color{red}{7}x & = &-15\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-15}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-4}& = &9 \\\Leftrightarrow & -x \color{red}{-4}\color{blue}{+4} & = &9\color{blue}{+4} \\\Leftrightarrow &-x & = &13\\\Leftrightarrow & \color{red}{-}x & = &13\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{13}{-1} \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-12}& = &-2 \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12} & = &-2\color{blue}{+12} \\\Leftrightarrow &-5x & = &10\\\Leftrightarrow & \color{red}{-5}x & = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)