Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & x \color{red}{-8}& = &-4 \\\Leftrightarrow & x \color{red}{-8}\color{blue}{+8} & = &-4\color{blue}{+8} \\\Leftrightarrow &x & = &4\\\Leftrightarrow & \color{red}{}x & = &4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 4 \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-13}& = &-10 \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13} & = &-10\color{blue}{+13} \\\Leftrightarrow &3x & = &3\\\Leftrightarrow & \color{red}{3}x & = &3\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{3}{3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+4}& = &-2 \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4} & = &-2\color{blue}{-4} \\\Leftrightarrow &15x & = &-6\\\Leftrightarrow & \color{red}{15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-6}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+11}& = &-13 \\\Leftrightarrow & 14x \color{red}{+11}\color{blue}{-11} & = &-13\color{blue}{-11} \\\Leftrightarrow &14x & = &-24\\\Leftrightarrow & \color{red}{14}x & = &-24\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-24}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-13}& = &12 \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13} & = &12\color{blue}{+13} \\\Leftrightarrow &12x & = &25\\\Leftrightarrow & \color{red}{12}x & = &25\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{25}{12} \\\Leftrightarrow & \color{green}{ x = \frac{25}{12} } & & \\ & V = \left\{ \frac{25}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+9}& = &-14 \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9} & = &-14\color{blue}{-9} \\\Leftrightarrow &3x & = &-23\\\Leftrightarrow & \color{red}{3}x & = &-23\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-23}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{3} } & & \\ & V = \left\{ \frac{-23}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-14}& = &-11 \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14} & = &-11\color{blue}{+14} \\\Leftrightarrow &-6x & = &3\\\Leftrightarrow & \color{red}{-6}x & = &3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+13}& = &-14 \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13} & = &-14\color{blue}{-13} \\\Leftrightarrow &9x & = &-27\\\Leftrightarrow & \color{red}{9}x & = &-27\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-27}{9} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{+8}& = &-11 \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8} & = &-11\color{blue}{-8} \\\Leftrightarrow &2x & = &-19\\\Leftrightarrow & \color{red}{2}x & = &-19\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-19}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{2} } & & \\ & V = \left\{ \frac{-19}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-1}& = &-10 \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1} & = &-10\color{blue}{+1} \\\Leftrightarrow &12x & = &-9\\\Leftrightarrow & \color{red}{12}x & = &-9\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-9}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{-9}& = &-14 \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9} & = &-14\color{blue}{+9} \\\Leftrightarrow &11x & = &-5\\\Leftrightarrow & \color{red}{11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-7}& = &14 \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7} & = &14\color{blue}{+7} \\\Leftrightarrow &-3x & = &21\\\Leftrightarrow & \color{red}{-3}x & = &21\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{21}{-3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)