Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+4}& = &7 \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4} & = &7\color{blue}{-4} \\\Leftrightarrow &6x & = &3\\\Leftrightarrow & \color{red}{6}x & = &3\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{3}{6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+2}& = &12 \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2} & = &12\color{blue}{-2} \\\Leftrightarrow &-6x & = &10\\\Leftrightarrow & \color{red}{-6}x & = &10\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{10}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-4}& = &-14 \\\Leftrightarrow & -x \color{red}{-4}\color{blue}{+4} & = &-14\color{blue}{+4} \\\Leftrightarrow &-x & = &-10\\\Leftrightarrow & \color{red}{-}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-10}{-1} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+1}& = &4 \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1} & = &4\color{blue}{-1} \\\Leftrightarrow &12x & = &3\\\Leftrightarrow & \color{red}{12}x & = &3\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{3}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{-13}& = &-3 \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13} & = &-3\color{blue}{+13} \\\Leftrightarrow &-4x & = &10\\\Leftrightarrow & \color{red}{-4}x & = &10\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{10}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+7}& = &-10 \\\Leftrightarrow & -x \color{red}{+7}\color{blue}{-7} & = &-10\color{blue}{-7} \\\Leftrightarrow &-x & = &-17\\\Leftrightarrow & \color{red}{-}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-17}{-1} \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+4}& = &-9 \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4} & = &-9\color{blue}{-4} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-3}& = &6 \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3} & = &6\color{blue}{+3} \\\Leftrightarrow &5x & = &9\\\Leftrightarrow & \color{red}{5}x & = &9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+7}& = &3 \\\Leftrightarrow & -13x \color{red}{+7}\color{blue}{-7} & = &3\color{blue}{-7} \\\Leftrightarrow &-13x & = &-4\\\Leftrightarrow & \color{red}{-13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-3}& = &13 \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3} & = &13\color{blue}{+3} \\\Leftrightarrow &12x & = &16\\\Leftrightarrow & \color{red}{12}x & = &16\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{16}{12} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{+10}& = &5 \\\Leftrightarrow & 2x \color{red}{+10}\color{blue}{-10} & = &5\color{blue}{-10} \\\Leftrightarrow &2x & = &-5\\\Leftrightarrow & \color{red}{2}x & = &-5\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-5}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{+6}& = &15 \\\Leftrightarrow & -3x \color{red}{+6}\color{blue}{-6} & = &15\color{blue}{-6} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)