Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{+10}& = &-8 \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10} & = &-8\color{blue}{-10} \\\Leftrightarrow &-5x & = &-18\\\Leftrightarrow & \color{red}{-5}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-15}& = &-8 \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15} & = &-8\color{blue}{+15} \\\Leftrightarrow &14x & = &7\\\Leftrightarrow & \color{red}{14}x & = &7\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{7}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+12}& = &-9 \\\Leftrightarrow & -10x \color{red}{+12}\color{blue}{-12} & = &-9\color{blue}{-12} \\\Leftrightarrow &-10x & = &-21\\\Leftrightarrow & \color{red}{-10}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-21}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{21}{10} } & & \\ & V = \left\{ \frac{21}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+1}& = &14 \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1} & = &14\color{blue}{-1} \\\Leftrightarrow &13x & = &13\\\Leftrightarrow & \color{red}{13}x & = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+3}& = &15 \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3} & = &15\color{blue}{-3} \\\Leftrightarrow &10x & = &12\\\Leftrightarrow & \color{red}{10}x & = &12\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{12}{10} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-12}& = &-8 \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12} & = &-8\color{blue}{+12} \\\Leftrightarrow &14x & = &4\\\Leftrightarrow & \color{red}{14}x & = &4\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{4}{14} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-13}& = &-1 \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13} & = &-1\color{blue}{+13} \\\Leftrightarrow &-4x & = &12\\\Leftrightarrow & \color{red}{-4}x & = &12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{12}{-4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-15}& = &11 \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15} & = &11\color{blue}{+15} \\\Leftrightarrow &-6x & = &26\\\Leftrightarrow & \color{red}{-6}x & = &26\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{26}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-2}& = &7 \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2} & = &7\color{blue}{+2} \\\Leftrightarrow &-6x & = &9\\\Leftrightarrow & \color{red}{-6}x & = &9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+2}& = &-10 \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2} & = &-10\color{blue}{-2} \\\Leftrightarrow &-6x & = &-12\\\Leftrightarrow & \color{red}{-6}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-12}{-6} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-14}& = &-8 \\\Leftrightarrow & 14x \color{red}{-14}\color{blue}{+14} & = &-8\color{blue}{+14} \\\Leftrightarrow &14x & = &6\\\Leftrightarrow & \color{red}{14}x & = &6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+14}& = &-5 \\\Leftrightarrow & 5x \color{red}{+14}\color{blue}{-14} & = &-5\color{blue}{-14} \\\Leftrightarrow &5x & = &-19\\\Leftrightarrow & \color{red}{5}x & = &-19\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-19}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{5} } & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)