Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & x \color{red}{+9}& = &-2 \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9} & = &-2\color{blue}{-9} \\\Leftrightarrow &x & = &-11\\\Leftrightarrow & \color{red}{}x & = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-6}& = &-5 \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6} & = &-5\color{blue}{+6} \\\Leftrightarrow &8x & = &1\\\Leftrightarrow & \color{red}{8}x & = &1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-2}& = &9 \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2} & = &9\color{blue}{+2} \\\Leftrightarrow &-6x & = &11\\\Leftrightarrow & \color{red}{-6}x & = &11\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{11}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{+15}& = &-2 \\\Leftrightarrow & -15x \color{red}{+15}\color{blue}{-15} & = &-2\color{blue}{-15} \\\Leftrightarrow &-15x & = &-17\\\Leftrightarrow & \color{red}{-15}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{17}{15} } & & \\ & V = \left\{ \frac{17}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-3}& = &14 \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3} & = &14\color{blue}{+3} \\\Leftrightarrow &-7x & = &17\\\Leftrightarrow & \color{red}{-7}x & = &17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+3}& = &-2 \\\Leftrightarrow & 2x \color{red}{+3}\color{blue}{-3} & = &-2\color{blue}{-3} \\\Leftrightarrow &2x & = &-5\\\Leftrightarrow & \color{red}{2}x & = &-5\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-5}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+8}& = &12 \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8} & = &12\color{blue}{-8} \\\Leftrightarrow &9x & = &4\\\Leftrightarrow & \color{red}{9}x & = &4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-7}& = &-11 \\\Leftrightarrow & 9x \color{red}{-7}\color{blue}{+7} & = &-11\color{blue}{+7} \\\Leftrightarrow &9x & = &-4\\\Leftrightarrow & \color{red}{9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{-5}& = &13 \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5} & = &13\color{blue}{+5} \\\Leftrightarrow &-12x & = &18\\\Leftrightarrow & \color{red}{-12}x & = &18\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{18}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+6}& = &-9 \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6} & = &-9\color{blue}{-6} \\\Leftrightarrow &15x & = &-15\\\Leftrightarrow & \color{red}{15}x & = &-15\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-15}{15} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+6}& = &-9 \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6} & = &-9\color{blue}{-6} \\\Leftrightarrow &3x & = &-15\\\Leftrightarrow & \color{red}{3}x & = &-15\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-15}{3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{-6}& = &-2 \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6} & = &-2\color{blue}{+6} \\\Leftrightarrow &14x & = &4\\\Leftrightarrow & \color{red}{14}x & = &4\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{4}{14} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)