Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-15}& = &7 \\\Leftrightarrow & -9x \color{red}{-15}\color{blue}{+15} & = &7\color{blue}{+15} \\\Leftrightarrow &-9x & = &22\\\Leftrightarrow & \color{red}{-9}x & = &22\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{22}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{9} } & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+9}& = &-10 \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9} & = &-10\color{blue}{-9} \\\Leftrightarrow &15x & = &-19\\\Leftrightarrow & \color{red}{15}x & = &-19\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-19}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{15} } & & \\ & V = \left\{ \frac{-19}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+6}& = &2 \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6} & = &2\color{blue}{-6} \\\Leftrightarrow &15x & = &-4\\\Leftrightarrow & \color{red}{15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-4}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-8}& = &-9 \\\Leftrightarrow & 6x \color{red}{-8}\color{blue}{+8} & = &-9\color{blue}{+8} \\\Leftrightarrow &6x & = &-1\\\Leftrightarrow & \color{red}{6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-1}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-5}& = &-15 \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5} & = &-15\color{blue}{+5} \\\Leftrightarrow &-x & = &-10\\\Leftrightarrow & \color{red}{-}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-10}{-1} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+1}& = &10 \\\Leftrightarrow & -10x \color{red}{+1}\color{blue}{-1} & = &10\color{blue}{-1} \\\Leftrightarrow &-10x & = &9\\\Leftrightarrow & \color{red}{-10}x & = &9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+11}& = &4 \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11} & = &4\color{blue}{-11} \\\Leftrightarrow &-10x & = &-7\\\Leftrightarrow & \color{red}{-10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{+1}& = &-9 \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1} & = &-9\color{blue}{-1} \\\Leftrightarrow &-6x & = &-10\\\Leftrightarrow & \color{red}{-6}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-10}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-12}& = &-4 \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12} & = &-4\color{blue}{+12} \\\Leftrightarrow &7x & = &8\\\Leftrightarrow & \color{red}{7}x & = &8\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{8}{7} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+10}& = &-10 \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10} & = &-10\color{blue}{-10} \\\Leftrightarrow &-5x & = &-20\\\Leftrightarrow & \color{red}{-5}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-20}{-5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{-9}& = &10 \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9} & = &10\color{blue}{+9} \\\Leftrightarrow &12x & = &19\\\Leftrightarrow & \color{red}{12}x & = &19\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{19}{12} \\\Leftrightarrow & \color{green}{ x = \frac{19}{12} } & & \\ & V = \left\{ \frac{19}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+1}& = &-1 \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1} & = &-1\color{blue}{-1} \\\Leftrightarrow &15x & = &-2\\\Leftrightarrow & \color{red}{15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)