Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+14}& = &1 \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14} & = &1\color{blue}{-14} \\\Leftrightarrow &-9x & = &-13\\\Leftrightarrow & \color{red}{-9}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+8}& = &-3 \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8} & = &-3\color{blue}{-8} \\\Leftrightarrow &10x & = &-11\\\Leftrightarrow & \color{red}{10}x & = &-11\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-11}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{10} } & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-14}& = &4 \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14} & = &4\color{blue}{+14} \\\Leftrightarrow &15x & = &18\\\Leftrightarrow & \color{red}{15}x & = &18\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{18}{15} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+10}& = &-13 \\\Leftrightarrow & 6x \color{red}{+10}\color{blue}{-10} & = &-13\color{blue}{-10} \\\Leftrightarrow &6x & = &-23\\\Leftrightarrow & \color{red}{6}x & = &-23\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-23}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{6} } & & \\ & V = \left\{ \frac{-23}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-7}& = &7 \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7} & = &7\color{blue}{+7} \\\Leftrightarrow &-11x & = &14\\\Leftrightarrow & \color{red}{-11}x & = &14\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{14}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-15}& = &-12 \\\Leftrightarrow & -9x \color{red}{-15}\color{blue}{+15} & = &-12\color{blue}{+15} \\\Leftrightarrow &-9x & = &3\\\Leftrightarrow & \color{red}{-9}x & = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+6}& = &-5 \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6} & = &-5\color{blue}{-6} \\\Leftrightarrow &-x & = &-11\\\Leftrightarrow & \color{red}{-}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-11}{-1} \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+2}& = &11 \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2} & = &11\color{blue}{-2} \\\Leftrightarrow &4x & = &9\\\Leftrightarrow & \color{red}{4}x & = &9\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{9}{4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{-2}& = &1 \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2} & = &1\color{blue}{+2} \\\Leftrightarrow &14x & = &3\\\Leftrightarrow & \color{red}{14}x & = &3\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{3}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+4}& = &10 \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4} & = &10\color{blue}{-4} \\\Leftrightarrow &-15x & = &6\\\Leftrightarrow & \color{red}{-15}x & = &6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+10}& = &-7 \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10} & = &-7\color{blue}{-10} \\\Leftrightarrow &-3x & = &-17\\\Leftrightarrow & \color{red}{-3}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-17}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{17}{3} } & & \\ & V = \left\{ \frac{17}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-1}& = &-13 \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1} & = &-13\color{blue}{+1} \\\Leftrightarrow &-12x & = &-12\\\Leftrightarrow & \color{red}{-12}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-12}{-12} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)