Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+1}& = &10 \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1} & = &10\color{blue}{-1} \\\Leftrightarrow &-7x & = &9\\\Leftrightarrow & \color{red}{-7}x & = &9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-9}& = &5 \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9} & = &5\color{blue}{+9} \\\Leftrightarrow &-9x & = &14\\\Leftrightarrow & \color{red}{-9}x & = &14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-8}& = &-10 \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8} & = &-10\color{blue}{+8} \\\Leftrightarrow &2x & = &-2\\\Leftrightarrow & \color{red}{2}x & = &-2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-2}{2} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+12}& = &15 \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12} & = &15\color{blue}{-12} \\\Leftrightarrow &5x & = &3\\\Leftrightarrow & \color{red}{5}x & = &3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+8}& = &10 \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8} & = &10\color{blue}{-8} \\\Leftrightarrow &4x & = &2\\\Leftrightarrow & \color{red}{4}x & = &2\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{2}{4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+3}& = &-15 \\\Leftrightarrow & 13x \color{red}{+3}\color{blue}{-3} & = &-15\color{blue}{-3} \\\Leftrightarrow &13x & = &-18\\\Leftrightarrow & \color{red}{13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-18}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{13} } & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+14}& = &-4 \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14} & = &-4\color{blue}{-14} \\\Leftrightarrow &14x & = &-18\\\Leftrightarrow & \color{red}{14}x & = &-18\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-18}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+11}& = &12 \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11} & = &12\color{blue}{-11} \\\Leftrightarrow &-10x & = &1\\\Leftrightarrow & \color{red}{-10}x & = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-9}& = &13 \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9} & = &13\color{blue}{+9} \\\Leftrightarrow &-14x & = &22\\\Leftrightarrow & \color{red}{-14}x & = &22\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{22}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-14}& = &2 \\\Leftrightarrow & -4x \color{red}{-14}\color{blue}{+14} & = &2\color{blue}{+14} \\\Leftrightarrow &-4x & = &16\\\Leftrightarrow & \color{red}{-4}x & = &16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{16}{-4} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{-4}& = &13 \\\Leftrightarrow & 12x \color{red}{-4}\color{blue}{+4} & = &13\color{blue}{+4} \\\Leftrightarrow &12x & = &17\\\Leftrightarrow & \color{red}{12}x & = &17\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{17}{12} \\\Leftrightarrow & \color{green}{ x = \frac{17}{12} } & & \\ & V = \left\{ \frac{17}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+9}& = &-8 \\\Leftrightarrow & -x \color{red}{+9}\color{blue}{-9} & = &-8\color{blue}{-9} \\\Leftrightarrow &-x & = &-17\\\Leftrightarrow & \color{red}{-}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-17}{-1} \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)