Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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