Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-7}& = &3 \\\Leftrightarrow & 2x \color{red}{-7}\color{blue}{+7} & = &3\color{blue}{+7} \\\Leftrightarrow &2x & = &10\\\Leftrightarrow & \color{red}{2}x & = &10\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{10}{2} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-14}& = &-13 \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14} & = &-13\color{blue}{+14} \\\Leftrightarrow &11x & = &1\\\Leftrightarrow & \color{red}{11}x & = &1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-8}& = &14 \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8} & = &14\color{blue}{+8} \\\Leftrightarrow &-7x & = &22\\\Leftrightarrow & \color{red}{-7}x & = &22\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{22}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+12}& = &-2 \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12} & = &-2\color{blue}{-12} \\\Leftrightarrow &8x & = &-14\\\Leftrightarrow & \color{red}{8}x & = &-14\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-14}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-7}& = &3 \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7} & = &3\color{blue}{+7} \\\Leftrightarrow &13x & = &10\\\Leftrightarrow & \color{red}{13}x & = &10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-1}& = &8 \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1} & = &8\color{blue}{+1} \\\Leftrightarrow &-5x & = &9\\\Leftrightarrow & \color{red}{-5}x & = &9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+8}& = &9 \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8} & = &9\color{blue}{-8} \\\Leftrightarrow &-14x & = &1\\\Leftrightarrow & \color{red}{-14}x & = &1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-12}& = &12 \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12} & = &12\color{blue}{+12} \\\Leftrightarrow &-8x & = &24\\\Leftrightarrow & \color{red}{-8}x & = &24\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{24}{-8} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+11}& = &-2 \\\Leftrightarrow & 6x \color{red}{+11}\color{blue}{-11} & = &-2\color{blue}{-11} \\\Leftrightarrow &6x & = &-13\\\Leftrightarrow & \color{red}{6}x & = &-13\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-13}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+15}& = &1 \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15} & = &1\color{blue}{-15} \\\Leftrightarrow &11x & = &-14\\\Leftrightarrow & \color{red}{11}x & = &-14\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-14}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-11}& = &-8 \\\Leftrightarrow & -12x \color{red}{-11}\color{blue}{+11} & = &-8\color{blue}{+11} \\\Leftrightarrow &-12x & = &3\\\Leftrightarrow & \color{red}{-12}x & = &3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-10}& = &-8 \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10} & = &-8\color{blue}{+10} \\\Leftrightarrow &-14x & = &2\\\Leftrightarrow & \color{red}{-14}x & = &2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)