Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+6}& = &8 \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6} & = &8\color{blue}{-6} \\\Leftrightarrow &-x & = &2\\\Leftrightarrow & \color{red}{-}x & = &2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{2}{-1} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+2}& = &7 \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2} & = &7\color{blue}{-2} \\\Leftrightarrow &11x & = &5\\\Leftrightarrow & \color{red}{11}x & = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-15}& = &-2 \\\Leftrightarrow & -x \color{red}{-15}\color{blue}{+15} & = &-2\color{blue}{+15} \\\Leftrightarrow &-x & = &13\\\Leftrightarrow & \color{red}{-}x & = &13\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{13}{-1} \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-12}& = &-13 \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12} & = &-13\color{blue}{+12} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-4}& = &-15 \\\Leftrightarrow & 12x \color{red}{-4}\color{blue}{+4} & = &-15\color{blue}{+4} \\\Leftrightarrow &12x & = &-11\\\Leftrightarrow & \color{red}{12}x & = &-11\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-11}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{12} } & & \\ & V = \left\{ \frac{-11}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-13}& = &11 \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13} & = &11\color{blue}{+13} \\\Leftrightarrow &12x & = &24\\\Leftrightarrow & \color{red}{12}x & = &24\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{24}{12} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+13}& = &-9 \\\Leftrightarrow & -3x \color{red}{+13}\color{blue}{-13} & = &-9\color{blue}{-13} \\\Leftrightarrow &-3x & = &-22\\\Leftrightarrow & \color{red}{-3}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-22}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{22}{3} } & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+15}& = &-3 \\\Leftrightarrow & -2x \color{red}{+15}\color{blue}{-15} & = &-3\color{blue}{-15} \\\Leftrightarrow &-2x & = &-18\\\Leftrightarrow & \color{red}{-2}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-18}{-2} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{+3}& = &13 \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3} & = &13\color{blue}{-3} \\\Leftrightarrow &-9x & = &10\\\Leftrightarrow & \color{red}{-9}x & = &10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+8}& = &-12 \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8} & = &-12\color{blue}{-8} \\\Leftrightarrow &-14x & = &-20\\\Leftrightarrow & \color{red}{-14}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-20}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+1}& = &8 \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1} & = &8\color{blue}{-1} \\\Leftrightarrow &-14x & = &7\\\Leftrightarrow & \color{red}{-14}x & = &7\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{7}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-13}& = &9 \\\Leftrightarrow & 4x \color{red}{-13}\color{blue}{+13} & = &9\color{blue}{+13} \\\Leftrightarrow &4x & = &22\\\Leftrightarrow & \color{red}{4}x & = &22\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{22}{4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)