Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{+12}& = &9 \\\Leftrightarrow & 4x \color{red}{+12}\color{blue}{-12} & = &9\color{blue}{-12} \\\Leftrightarrow &4x & = &-3\\\Leftrightarrow & \color{red}{4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-12}& = &15 \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12} & = &15\color{blue}{+12} \\\Leftrightarrow &6x & = &27\\\Leftrightarrow & \color{red}{6}x & = &27\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{27}{6} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+7}& = &-12 \\\Leftrightarrow & 4x \color{red}{+7}\color{blue}{-7} & = &-12\color{blue}{-7} \\\Leftrightarrow &4x & = &-19\\\Leftrightarrow & \color{red}{4}x & = &-19\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-19}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{4} } & & \\ & V = \left\{ \frac{-19}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-9}& = &-9 \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9} & = &-9\color{blue}{+9} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+14}& = &-5 \\\Leftrightarrow & -4x \color{red}{+14}\color{blue}{-14} & = &-5\color{blue}{-14} \\\Leftrightarrow &-4x & = &-19\\\Leftrightarrow & \color{red}{-4}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{19}{4} } & & \\ & V = \left\{ \frac{19}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-9}& = &-1 \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9} & = &-1\color{blue}{+9} \\\Leftrightarrow &-5x & = &8\\\Leftrightarrow & \color{red}{-5}x & = &8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+7}& = &14 \\\Leftrightarrow & -2x \color{red}{+7}\color{blue}{-7} & = &14\color{blue}{-7} \\\Leftrightarrow &-2x & = &7\\\Leftrightarrow & \color{red}{-2}x & = &7\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{7}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-6}& = &-1 \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6} & = &-1\color{blue}{+6} \\\Leftrightarrow &-15x & = &5\\\Leftrightarrow & \color{red}{-15}x & = &5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+3}& = &12 \\\Leftrightarrow & 14x \color{red}{+3}\color{blue}{-3} & = &12\color{blue}{-3} \\\Leftrightarrow &14x & = &9\\\Leftrightarrow & \color{red}{14}x & = &9\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{9}{14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+4}& = &-4 \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4} & = &-4\color{blue}{-4} \\\Leftrightarrow &-2x & = &-8\\\Leftrightarrow & \color{red}{-2}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-8}{-2} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+6}& = &-4 \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6} & = &-4\color{blue}{-6} \\\Leftrightarrow &3x & = &-10\\\Leftrightarrow & \color{red}{3}x & = &-10\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-10}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+3}& = &-14 \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3} & = &-14\color{blue}{-3} \\\Leftrightarrow &-5x & = &-17\\\Leftrightarrow & \color{red}{-5}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-17}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{17}{5} } & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)