Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-8}& = &11 \\\Leftrightarrow & 8x \color{red}{-8}\color{blue}{+8} & = &11\color{blue}{+8} \\\Leftrightarrow &8x & = &19\\\Leftrightarrow & \color{red}{8}x & = &19\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{19}{8} \\\Leftrightarrow & \color{green}{ x = \frac{19}{8} } & & \\ & V = \left\{ \frac{19}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-15}& = &-3 \\\Leftrightarrow & 4x \color{red}{-15}\color{blue}{+15} & = &-3\color{blue}{+15} \\\Leftrightarrow &4x & = &12\\\Leftrightarrow & \color{red}{4}x & = &12\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{12}{4} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-6}& = &3 \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6} & = &3\color{blue}{+6} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{+4}& = &-12 \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4} & = &-12\color{blue}{-4} \\\Leftrightarrow &7x & = &-16\\\Leftrightarrow & \color{red}{7}x & = &-16\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-16}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{7} } & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{+8}& = &6 \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8} & = &6\color{blue}{-8} \\\Leftrightarrow &11x & = &-2\\\Leftrightarrow & \color{red}{11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+3}& = &10 \\\Leftrightarrow & -8x \color{red}{+3}\color{blue}{-3} & = &10\color{blue}{-3} \\\Leftrightarrow &-8x & = &7\\\Leftrightarrow & \color{red}{-8}x & = &7\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{7}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+14}& = &11 \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14} & = &11\color{blue}{-14} \\\Leftrightarrow &-9x & = &-3\\\Leftrightarrow & \color{red}{-9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-8}& = &-11 \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8} & = &-11\color{blue}{+8} \\\Leftrightarrow &9x & = &-3\\\Leftrightarrow & \color{red}{9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-3}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+11}& = &-5 \\\Leftrightarrow & 10x \color{red}{+11}\color{blue}{-11} & = &-5\color{blue}{-11} \\\Leftrightarrow &10x & = &-16\\\Leftrightarrow & \color{red}{10}x & = &-16\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-16}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+10}& = &11 \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10} & = &11\color{blue}{-10} \\\Leftrightarrow &5x & = &1\\\Leftrightarrow & \color{red}{5}x & = &1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+13}& = &14 \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13} & = &14\color{blue}{-13} \\\Leftrightarrow &11x & = &1\\\Leftrightarrow & \color{red}{11}x & = &1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+14}& = &-7 \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14} & = &-7\color{blue}{-14} \\\Leftrightarrow &11x & = &-21\\\Leftrightarrow & \color{red}{11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-21}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{11} } & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)