Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+1}& = &-10 \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1} & = &-10\color{blue}{-1} \\\Leftrightarrow &-x & = &-11\\\Leftrightarrow & \color{red}{-}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-11}{-1} \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+6}& = &-2 \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6} & = &-2\color{blue}{-6} \\\Leftrightarrow &15x & = &-8\\\Leftrightarrow & \color{red}{15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-8}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+10}& = &3 \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10} & = &3\color{blue}{-10} \\\Leftrightarrow &-9x & = &-7\\\Leftrightarrow & \color{red}{-9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{-3}& = &11 \\\Leftrightarrow & 8x \color{red}{-3}\color{blue}{+3} & = &11\color{blue}{+3} \\\Leftrightarrow &8x & = &14\\\Leftrightarrow & \color{red}{8}x & = &14\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{14}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+3}& = &-2 \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3} & = &-2\color{blue}{-3} \\\Leftrightarrow &-9x & = &-5\\\Leftrightarrow & \color{red}{-9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+6}& = &-1 \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6} & = &-1\color{blue}{-6} \\\Leftrightarrow &15x & = &-7\\\Leftrightarrow & \color{red}{15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+12}& = &-9 \\\Leftrightarrow & -10x \color{red}{+12}\color{blue}{-12} & = &-9\color{blue}{-12} \\\Leftrightarrow &-10x & = &-21\\\Leftrightarrow & \color{red}{-10}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-21}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{21}{10} } & & \\ & V = \left\{ \frac{21}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+11}& = &-9 \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11} & = &-9\color{blue}{-11} \\\Leftrightarrow &-8x & = &-20\\\Leftrightarrow & \color{red}{-8}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-5}& = &-12 \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5} & = &-12\color{blue}{+5} \\\Leftrightarrow &8x & = &-7\\\Leftrightarrow & \color{red}{8}x & = &-7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+10}& = &12 \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10} & = &12\color{blue}{-10} \\\Leftrightarrow &5x & = &2\\\Leftrightarrow & \color{red}{5}x & = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-10}& = &-15 \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10} & = &-15\color{blue}{+10} \\\Leftrightarrow &10x & = &-5\\\Leftrightarrow & \color{red}{10}x & = &-5\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-5}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+13}& = &-7 \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13} & = &-7\color{blue}{-13} \\\Leftrightarrow &11x & = &-20\\\Leftrightarrow & \color{red}{11}x & = &-20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)