Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-2}& = &-12 \\\Leftrightarrow & 2x \color{red}{-2}\color{blue}{+2} & = &-12\color{blue}{+2} \\\Leftrightarrow &2x & = &-10\\\Leftrightarrow & \color{red}{2}x & = &-10\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-10}{2} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-4}& = &-12 \\\Leftrightarrow & -2x \color{red}{-4}\color{blue}{+4} & = &-12\color{blue}{+4} \\\Leftrightarrow &-2x & = &-8\\\Leftrightarrow & \color{red}{-2}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-8}{-2} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+3}& = &-9 \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3} & = &-9\color{blue}{-3} \\\Leftrightarrow &x & = &-12\\\Leftrightarrow & \color{red}{}x & = &-12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -12 \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+14}& = &6 \\\Leftrightarrow & -11x \color{red}{+14}\color{blue}{-14} & = &6\color{blue}{-14} \\\Leftrightarrow &-11x & = &-8\\\Leftrightarrow & \color{red}{-11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-5}& = &13 \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5} & = &13\color{blue}{+5} \\\Leftrightarrow &-8x & = &18\\\Leftrightarrow & \color{red}{-8}x & = &18\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{18}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{+3}& = &8 \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3} & = &8\color{blue}{-3} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-15}& = &-15 \\\Leftrightarrow & 12x \color{red}{-15}\color{blue}{+15} & = &-15\color{blue}{+15} \\\Leftrightarrow &12x & = &0\\\Leftrightarrow & \color{red}{12}x & = &0\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{0}{12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-3}& = &7 \\\Leftrightarrow & -8x \color{red}{-3}\color{blue}{+3} & = &7\color{blue}{+3} \\\Leftrightarrow &-8x & = &10\\\Leftrightarrow & \color{red}{-8}x & = &10\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{10}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-9}& = &-1 \\\Leftrightarrow & 2x \color{red}{-9}\color{blue}{+9} & = &-1\color{blue}{+9} \\\Leftrightarrow &2x & = &8\\\Leftrightarrow & \color{red}{2}x & = &8\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{8}{2} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{+2}& = &-11 \\\Leftrightarrow & -13x \color{red}{+2}\color{blue}{-2} & = &-11\color{blue}{-2} \\\Leftrightarrow &-13x & = &-13\\\Leftrightarrow & \color{red}{-13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-13}{-13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-6}& = &8 \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6} & = &8\color{blue}{+6} \\\Leftrightarrow &-6x & = &14\\\Leftrightarrow & \color{red}{-6}x & = &14\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{14}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-9}& = &2 \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9} & = &2\color{blue}{+9} \\\Leftrightarrow &12x & = &11\\\Leftrightarrow & \color{red}{12}x & = &11\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{11}{12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{12} } & & \\ & V = \left\{ \frac{11}{12} \right\} & \\\end{align}\)