Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & x \color{red}{+3}& = &-9 \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3} & = &-9\color{blue}{-3} \\\Leftrightarrow &x & = &-12\\\Leftrightarrow & \color{red}{}x & = &-12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -12 \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-13}& = &-15 \\\Leftrightarrow & -15x \color{red}{-13}\color{blue}{+13} & = &-15\color{blue}{+13} \\\Leftrightarrow &-15x & = &-2\\\Leftrightarrow & \color{red}{-15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+15}& = &5 \\\Leftrightarrow & 5x \color{red}{+15}\color{blue}{-15} & = &5\color{blue}{-15} \\\Leftrightarrow &5x & = &-10\\\Leftrightarrow & \color{red}{5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-10}{5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+13}& = &-6 \\\Leftrightarrow & -x \color{red}{+13}\color{blue}{-13} & = &-6\color{blue}{-13} \\\Leftrightarrow &-x & = &-19\\\Leftrightarrow & \color{red}{-}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-19}{-1} \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+7}& = &3 \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7} & = &3\color{blue}{-7} \\\Leftrightarrow &5x & = &-4\\\Leftrightarrow & \color{red}{5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{-11}& = &4 \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11} & = &4\color{blue}{+11} \\\Leftrightarrow &-14x & = &15\\\Leftrightarrow & \color{red}{-14}x & = &15\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{15}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{14} } & & \\ & V = \left\{ \frac{-15}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+10}& = &-9 \\\Leftrightarrow & 10x \color{red}{+10}\color{blue}{-10} & = &-9\color{blue}{-10} \\\Leftrightarrow &10x & = &-19\\\Leftrightarrow & \color{red}{10}x & = &-19\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-19}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{10} } & & \\ & V = \left\{ \frac{-19}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-13}& = &5 \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13} & = &5\color{blue}{+13} \\\Leftrightarrow &11x & = &18\\\Leftrightarrow & \color{red}{11}x & = &18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+3}& = &12 \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3} & = &12\color{blue}{-3} \\\Leftrightarrow &-6x & = &9\\\Leftrightarrow & \color{red}{-6}x & = &9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{+12}& = &-4 \\\Leftrightarrow & 4x \color{red}{+12}\color{blue}{-12} & = &-4\color{blue}{-12} \\\Leftrightarrow &4x & = &-16\\\Leftrightarrow & \color{red}{4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-16}{4} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-2}& = &14 \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2} & = &14\color{blue}{+2} \\\Leftrightarrow &10x & = &16\\\Leftrightarrow & \color{red}{10}x & = &16\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{16}{10} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+1}& = &4 \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1} & = &4\color{blue}{-1} \\\Leftrightarrow &6x & = &3\\\Leftrightarrow & \color{red}{6}x & = &3\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{3}{6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)