Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-3}& = &4 \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3} & = &4\color{blue}{+3} \\\Leftrightarrow &-13x & = &7\\\Leftrightarrow & \color{red}{-13}x & = &7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+6}& = &-7 \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6} & = &-7\color{blue}{-6} \\\Leftrightarrow &12x & = &-13\\\Leftrightarrow & \color{red}{12}x & = &-13\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-13}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{12} } & & \\ & V = \left\{ \frac{-13}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+8}& = &-9 \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8} & = &-9\color{blue}{-8} \\\Leftrightarrow &-2x & = &-17\\\Leftrightarrow & \color{red}{-2}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-17}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{17}{2} } & & \\ & V = \left\{ \frac{17}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+9}& = &-4 \\\Leftrightarrow & 5x \color{red}{+9}\color{blue}{-9} & = &-4\color{blue}{-9} \\\Leftrightarrow &5x & = &-13\\\Leftrightarrow & \color{red}{5}x & = &-13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-14}& = &9 \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14} & = &9\color{blue}{+14} \\\Leftrightarrow &13x & = &23\\\Leftrightarrow & \color{red}{13}x & = &23\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{23}{13} \\\Leftrightarrow & \color{green}{ x = \frac{23}{13} } & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-14}& = &9 \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14} & = &9\color{blue}{+14} \\\Leftrightarrow &-8x & = &23\\\Leftrightarrow & \color{red}{-8}x & = &23\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{23}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{8} } & & \\ & V = \left\{ \frac{-23}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+10}& = &-11 \\\Leftrightarrow & -7x \color{red}{+10}\color{blue}{-10} & = &-11\color{blue}{-10} \\\Leftrightarrow &-7x & = &-21\\\Leftrightarrow & \color{red}{-7}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-21}{-7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{-5}& = &1 \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5} & = &1\color{blue}{+5} \\\Leftrightarrow &15x & = &6\\\Leftrightarrow & \color{red}{15}x & = &6\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{6}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{-12}& = &-5 \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12} & = &-5\color{blue}{+12} \\\Leftrightarrow &-x & = &7\\\Leftrightarrow & \color{red}{-}x & = &7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{7}{-1} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{+4}& = &4 \\\Leftrightarrow & x \color{red}{+4}\color{blue}{-4} & = &4\color{blue}{-4} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-3}& = &-15 \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3} & = &-15\color{blue}{+3} \\\Leftrightarrow &-6x & = &-12\\\Leftrightarrow & \color{red}{-6}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-12}{-6} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-7}& = &6 \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7} & = &6\color{blue}{+7} \\\Leftrightarrow &13x & = &13\\\Leftrightarrow & \color{red}{13}x & = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)