Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+8}& = &-14 \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8} & = &-14\color{blue}{-8} \\\Leftrightarrow &-4x & = &-22\\\Leftrightarrow & \color{red}{-4}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-22}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-4}& = &-9 \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4} & = &-9\color{blue}{+4} \\\Leftrightarrow &-15x & = &-5\\\Leftrightarrow & \color{red}{-15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-5}& = &-9 \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5} & = &-9\color{blue}{+5} \\\Leftrightarrow &6x & = &-4\\\Leftrightarrow & \color{red}{6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-4}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{+14}& = &3 \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14} & = &3\color{blue}{-14} \\\Leftrightarrow &-9x & = &-11\\\Leftrightarrow & \color{red}{-9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+5}& = &15 \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5} & = &15\color{blue}{-5} \\\Leftrightarrow &12x & = &10\\\Leftrightarrow & \color{red}{12}x & = &10\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{10}{12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-3}& = &-12 \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3} & = &-12\color{blue}{+3} \\\Leftrightarrow &7x & = &-9\\\Leftrightarrow & \color{red}{7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+6}& = &-14 \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6} & = &-14\color{blue}{-6} \\\Leftrightarrow &7x & = &-20\\\Leftrightarrow & \color{red}{7}x & = &-20\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-20}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{7} } & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+11}& = &-5 \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11} & = &-5\color{blue}{-11} \\\Leftrightarrow &-8x & = &-16\\\Leftrightarrow & \color{red}{-8}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-16}{-8} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+2}& = &12 \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2} & = &12\color{blue}{-2} \\\Leftrightarrow &14x & = &10\\\Leftrightarrow & \color{red}{14}x & = &10\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{10}{14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-13}& = &15 \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13} & = &15\color{blue}{+13} \\\Leftrightarrow &-7x & = &28\\\Leftrightarrow & \color{red}{-7}x & = &28\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{28}{-7} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{+5}& = &3 \\\Leftrightarrow & -4x \color{red}{+5}\color{blue}{-5} & = &3\color{blue}{-5} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+7}& = &2 \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7} & = &2\color{blue}{-7} \\\Leftrightarrow &14x & = &-5\\\Leftrightarrow & \color{red}{14}x & = &-5\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-5}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{14} } & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)