Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{+15}& = &-13 \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15} & = &-13\color{blue}{-15} \\\Leftrightarrow &-11x & = &-28\\\Leftrightarrow & \color{red}{-11}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-28}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{28}{11} } & & \\ & V = \left\{ \frac{28}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+14}& = &-6 \\\Leftrightarrow & 8x \color{red}{+14}\color{blue}{-14} & = &-6\color{blue}{-14} \\\Leftrightarrow &8x & = &-20\\\Leftrightarrow & \color{red}{8}x & = &-20\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-20}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-8}& = &14 \\\Leftrightarrow & -x \color{red}{-8}\color{blue}{+8} & = &14\color{blue}{+8} \\\Leftrightarrow &-x & = &22\\\Leftrightarrow & \color{red}{-}x & = &22\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{22}{-1} \\\Leftrightarrow & \color{green}{ x = -22 } & & \\ & V = \left\{ -22 \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-7}& = &-5 \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7} & = &-5\color{blue}{+7} \\\Leftrightarrow &-6x & = &2\\\Leftrightarrow & \color{red}{-6}x & = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-7}& = &9 \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7} & = &9\color{blue}{+7} \\\Leftrightarrow &14x & = &16\\\Leftrightarrow & \color{red}{14}x & = &16\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{16}{14} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-11}& = &10 \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11} & = &10\color{blue}{+11} \\\Leftrightarrow &9x & = &21\\\Leftrightarrow & \color{red}{9}x & = &21\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{21}{9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-11}& = &10 \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11} & = &10\color{blue}{+11} \\\Leftrightarrow &-3x & = &21\\\Leftrightarrow & \color{red}{-3}x & = &21\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{21}{-3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{-4}& = &2 \\\Leftrightarrow & -x \color{red}{-4}\color{blue}{+4} & = &2\color{blue}{+4} \\\Leftrightarrow &-x & = &6\\\Leftrightarrow & \color{red}{-}x & = &6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{6}{-1} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+5}& = &1 \\\Leftrightarrow & 15x \color{red}{+5}\color{blue}{-5} & = &1\color{blue}{-5} \\\Leftrightarrow &15x & = &-4\\\Leftrightarrow & \color{red}{15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-4}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+8}& = &12 \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8} & = &12\color{blue}{-8} \\\Leftrightarrow &-6x & = &4\\\Leftrightarrow & \color{red}{-6}x & = &4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+8}& = &11 \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8} & = &11\color{blue}{-8} \\\Leftrightarrow &-14x & = &3\\\Leftrightarrow & \color{red}{-14}x & = &3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+8}& = &-3 \\\Leftrightarrow & 14x \color{red}{+8}\color{blue}{-8} & = &-3\color{blue}{-8} \\\Leftrightarrow &14x & = &-11\\\Leftrightarrow & \color{red}{14}x & = &-11\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-11}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)