Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+7}& = &2 \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7} & = &2\color{blue}{-7} \\\Leftrightarrow &-10x & = &-5\\\Leftrightarrow & \color{red}{-10}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{+7}& = &4 \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7} & = &4\color{blue}{-7} \\\Leftrightarrow &-14x & = &-3\\\Leftrightarrow & \color{red}{-14}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-1}& = &-7 \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1} & = &-7\color{blue}{+1} \\\Leftrightarrow &-5x & = &-6\\\Leftrightarrow & \color{red}{-5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+14}& = &-2 \\\Leftrightarrow & 8x \color{red}{+14}\color{blue}{-14} & = &-2\color{blue}{-14} \\\Leftrightarrow &8x & = &-16\\\Leftrightarrow & \color{red}{8}x & = &-16\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-16}{8} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-12}& = &8 \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12} & = &8\color{blue}{+12} \\\Leftrightarrow &-5x & = &20\\\Leftrightarrow & \color{red}{-5}x & = &20\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{20}{-5} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-14}& = &3 \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14} & = &3\color{blue}{+14} \\\Leftrightarrow &6x & = &17\\\Leftrightarrow & \color{red}{6}x & = &17\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{17}{6} \\\Leftrightarrow & \color{green}{ x = \frac{17}{6} } & & \\ & V = \left\{ \frac{17}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+11}& = &9 \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11} & = &9\color{blue}{-11} \\\Leftrightarrow &5x & = &-2\\\Leftrightarrow & \color{red}{5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+14}& = &-3 \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14} & = &-3\color{blue}{-14} \\\Leftrightarrow &-7x & = &-17\\\Leftrightarrow & \color{red}{-7}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-12}& = &-15 \\\Leftrightarrow & -10x \color{red}{-12}\color{blue}{+12} & = &-15\color{blue}{+12} \\\Leftrightarrow &-10x & = &-3\\\Leftrightarrow & \color{red}{-10}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{10} } & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+9}& = &-1 \\\Leftrightarrow & 10x \color{red}{+9}\color{blue}{-9} & = &-1\color{blue}{-9} \\\Leftrightarrow &10x & = &-10\\\Leftrightarrow & \color{red}{10}x & = &-10\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-10}{10} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-8}& = &-7 \\\Leftrightarrow & 6x \color{red}{-8}\color{blue}{+8} & = &-7\color{blue}{+8} \\\Leftrightarrow &6x & = &1\\\Leftrightarrow & \color{red}{6}x & = &1\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{1}{6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{+2}& = &-11 \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2} & = &-11\color{blue}{-2} \\\Leftrightarrow &-3x & = &-13\\\Leftrightarrow & \color{red}{-3}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)