Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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