Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{+7}& = &9 \\\Leftrightarrow & -2x \color{red}{+7}\color{blue}{-7} & = &9\color{blue}{-7} \\\Leftrightarrow &-2x & = &2\\\Leftrightarrow & \color{red}{-2}x & = &2\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{2}{-2} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+13}& = &-8 \\\Leftrightarrow & -11x \color{red}{+13}\color{blue}{-13} & = &-8\color{blue}{-13} \\\Leftrightarrow &-11x & = &-21\\\Leftrightarrow & \color{red}{-11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-8}& = &-14 \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8} & = &-14\color{blue}{+8} \\\Leftrightarrow &-7x & = &-6\\\Leftrightarrow & \color{red}{-7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-14}& = &4 \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14} & = &4\color{blue}{+14} \\\Leftrightarrow &2x & = &18\\\Leftrightarrow & \color{red}{2}x & = &18\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{18}{2} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+12}& = &-11 \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12} & = &-11\color{blue}{-12} \\\Leftrightarrow &6x & = &-23\\\Leftrightarrow & \color{red}{6}x & = &-23\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-23}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{6} } & & \\ & V = \left\{ \frac{-23}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+1}& = &-1 \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1} & = &-1\color{blue}{-1} \\\Leftrightarrow &6x & = &-2\\\Leftrightarrow & \color{red}{6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-2}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{+3}& = &-5 \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3} & = &-5\color{blue}{-3} \\\Leftrightarrow &4x & = &-8\\\Leftrightarrow & \color{red}{4}x & = &-8\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-8}{4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-9}& = &14 \\\Leftrightarrow & 5x \color{red}{-9}\color{blue}{+9} & = &14\color{blue}{+9} \\\Leftrightarrow &5x & = &23\\\Leftrightarrow & \color{red}{5}x & = &23\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{23}{5} \\\Leftrightarrow & \color{green}{ x = \frac{23}{5} } & & \\ & V = \left\{ \frac{23}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-13}& = &-10 \\\Leftrightarrow & 7x \color{red}{-13}\color{blue}{+13} & = &-10\color{blue}{+13} \\\Leftrightarrow &7x & = &3\\\Leftrightarrow & \color{red}{7}x & = &3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-8}& = &-7 \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8} & = &-7\color{blue}{+8} \\\Leftrightarrow &7x & = &1\\\Leftrightarrow & \color{red}{7}x & = &1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+9}& = &1 \\\Leftrightarrow & -5x \color{red}{+9}\color{blue}{-9} & = &1\color{blue}{-9} \\\Leftrightarrow &-5x & = &-8\\\Leftrightarrow & \color{red}{-5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+1}& = &-10 \\\Leftrightarrow & 11x \color{red}{+1}\color{blue}{-1} & = &-10\color{blue}{-1} \\\Leftrightarrow &11x & = &-11\\\Leftrightarrow & \color{red}{11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-11}{11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)