Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+5}& = &-10 \\\Leftrightarrow & -x \color{red}{+5}\color{blue}{-5} & = &-10\color{blue}{-5} \\\Leftrightarrow &-x & = &-15\\\Leftrightarrow & \color{red}{-}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-15}{-1} \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+6}& = &8 \\\Leftrightarrow & -10x \color{red}{+6}\color{blue}{-6} & = &8\color{blue}{-6} \\\Leftrightarrow &-10x & = &2\\\Leftrightarrow & \color{red}{-10}x & = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-12}& = &6 \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12} & = &6\color{blue}{+12} \\\Leftrightarrow &9x & = &18\\\Leftrightarrow & \color{red}{9}x & = &18\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{18}{9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-12}& = &-11 \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12} & = &-11\color{blue}{+12} \\\Leftrightarrow &-13x & = &1\\\Leftrightarrow & \color{red}{-13}x & = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-6}& = &10 \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6} & = &10\color{blue}{+6} \\\Leftrightarrow &13x & = &16\\\Leftrightarrow & \color{red}{13}x & = &16\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{16}{13} \\\Leftrightarrow & \color{green}{ x = \frac{16}{13} } & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-5}& = &-12 \\\Leftrightarrow & -10x \color{red}{-5}\color{blue}{+5} & = &-12\color{blue}{+5} \\\Leftrightarrow &-10x & = &-7\\\Leftrightarrow & \color{red}{-10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+11}& = &15 \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11} & = &15\color{blue}{-11} \\\Leftrightarrow &12x & = &4\\\Leftrightarrow & \color{red}{12}x & = &4\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{4}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+1}& = &-9 \\\Leftrightarrow & 10x \color{red}{+1}\color{blue}{-1} & = &-9\color{blue}{-1} \\\Leftrightarrow &10x & = &-10\\\Leftrightarrow & \color{red}{10}x & = &-10\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-10}{10} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+2}& = &-14 \\\Leftrightarrow & 7x \color{red}{+2}\color{blue}{-2} & = &-14\color{blue}{-2} \\\Leftrightarrow &7x & = &-16\\\Leftrightarrow & \color{red}{7}x & = &-16\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-16}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{7} } & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{+8}& = &4 \\\Leftrightarrow & x \color{red}{+8}\color{blue}{-8} & = &4\color{blue}{-8} \\\Leftrightarrow &x & = &-4\\\Leftrightarrow & \color{red}{}x & = &-4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -4 \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-2}& = &-3 \\\Leftrightarrow & -12x \color{red}{-2}\color{blue}{+2} & = &-3\color{blue}{+2} \\\Leftrightarrow &-12x & = &-1\\\Leftrightarrow & \color{red}{-12}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-14}& = &-14 \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14} & = &-14\color{blue}{+14} \\\Leftrightarrow &8x & = &0\\\Leftrightarrow & \color{red}{8}x & = &0\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{0}{8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)