Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-6}& = &10 \\\Leftrightarrow & 10x \color{red}{-6}\color{blue}{+6} & = &10\color{blue}{+6} \\\Leftrightarrow &10x & = &16\\\Leftrightarrow & \color{red}{10}x & = &16\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{16}{10} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+7}& = &14 \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7} & = &14\color{blue}{-7} \\\Leftrightarrow &14x & = &7\\\Leftrightarrow & \color{red}{14}x & = &7\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{7}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+14}& = &-15 \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14} & = &-15\color{blue}{-14} \\\Leftrightarrow &3x & = &-29\\\Leftrightarrow & \color{red}{3}x & = &-29\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-29}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{3} } & & \\ & V = \left\{ \frac{-29}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+5}& = &4 \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5} & = &4\color{blue}{-5} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+10}& = &-6 \\\Leftrightarrow & -12x \color{red}{+10}\color{blue}{-10} & = &-6\color{blue}{-10} \\\Leftrightarrow &-12x & = &-16\\\Leftrightarrow & \color{red}{-12}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{+12}& = &9 \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12} & = &9\color{blue}{-12} \\\Leftrightarrow &-4x & = &-3\\\Leftrightarrow & \color{red}{-4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-5}& = &-2 \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5} & = &-2\color{blue}{+5} \\\Leftrightarrow &-x & = &3\\\Leftrightarrow & \color{red}{-}x & = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+11}& = &6 \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11} & = &6\color{blue}{-11} \\\Leftrightarrow &-10x & = &-5\\\Leftrightarrow & \color{red}{-10}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-4}& = &-1 \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4} & = &-1\color{blue}{+4} \\\Leftrightarrow &15x & = &3\\\Leftrightarrow & \color{red}{15}x & = &3\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{3}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-12}& = &13 \\\Leftrightarrow & 8x \color{red}{-12}\color{blue}{+12} & = &13\color{blue}{+12} \\\Leftrightarrow &8x & = &25\\\Leftrightarrow & \color{red}{8}x & = &25\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{25}{8} \\\Leftrightarrow & \color{green}{ x = \frac{25}{8} } & & \\ & V = \left\{ \frac{25}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{-11}& = &-15 \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11} & = &-15\color{blue}{+11} \\\Leftrightarrow &12x & = &-4\\\Leftrightarrow & \color{red}{12}x & = &-4\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-4}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+12}& = &-12 \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12} & = &-12\color{blue}{-12} \\\Leftrightarrow &-8x & = &-24\\\Leftrightarrow & \color{red}{-8}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-24}{-8} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)