Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+4}& = &-13 \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4} & = &-13\color{blue}{-4} \\\Leftrightarrow &11x & = &-17\\\Leftrightarrow & \color{red}{11}x & = &-17\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-17}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+7}& = &3 \\\Leftrightarrow & -2x \color{red}{+7}\color{blue}{-7} & = &3\color{blue}{-7} \\\Leftrightarrow &-2x & = &-4\\\Leftrightarrow & \color{red}{-2}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-4}{-2} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-12}& = &4 \\\Leftrightarrow & -4x \color{red}{-12}\color{blue}{+12} & = &4\color{blue}{+12} \\\Leftrightarrow &-4x & = &16\\\Leftrightarrow & \color{red}{-4}x & = &16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{16}{-4} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-9}& = &8 \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9} & = &8\color{blue}{+9} \\\Leftrightarrow &-4x & = &17\\\Leftrightarrow & \color{red}{-4}x & = &17\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{17}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{4} } & & \\ & V = \left\{ \frac{-17}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{-5}& = &9 \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5} & = &9\color{blue}{+5} \\\Leftrightarrow &15x & = &14\\\Leftrightarrow & \color{red}{15}x & = &14\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{14}{15} \\\Leftrightarrow & \color{green}{ x = \frac{14}{15} } & & \\ & V = \left\{ \frac{14}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-13}& = &3 \\\Leftrightarrow & -x \color{red}{-13}\color{blue}{+13} & = &3\color{blue}{+13} \\\Leftrightarrow &-x & = &16\\\Leftrightarrow & \color{red}{-}x & = &16\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{16}{-1} \\\Leftrightarrow & \color{green}{ x = -16 } & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+13}& = &-9 \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13} & = &-9\color{blue}{-13} \\\Leftrightarrow &3x & = &-22\\\Leftrightarrow & \color{red}{3}x & = &-22\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-22}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{3} } & & \\ & V = \left\{ \frac{-22}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-8}& = &10 \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8} & = &10\color{blue}{+8} \\\Leftrightarrow &12x & = &18\\\Leftrightarrow & \color{red}{12}x & = &18\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{18}{12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{-12}& = &-4 \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12} & = &-4\color{blue}{+12} \\\Leftrightarrow &14x & = &8\\\Leftrightarrow & \color{red}{14}x & = &8\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{8}{14} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+11}& = &-13 \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11} & = &-13\color{blue}{-11} \\\Leftrightarrow &-x & = &-24\\\Leftrightarrow & \color{red}{-}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-24}{-1} \\\Leftrightarrow & \color{green}{ x = 24 } & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-8}& = &15 \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8} & = &15\color{blue}{+8} \\\Leftrightarrow &14x & = &23\\\Leftrightarrow & \color{red}{14}x & = &23\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{23}{14} \\\Leftrightarrow & \color{green}{ x = \frac{23}{14} } & & \\ & V = \left\{ \frac{23}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{-15}& = &7 \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15} & = &7\color{blue}{+15} \\\Leftrightarrow &10x & = &22\\\Leftrightarrow & \color{red}{10}x & = &22\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{22}{10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)