Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-13}& = &-15 \\\Leftrightarrow & -9x \color{red}{-13}\color{blue}{+13} & = &-15\color{blue}{+13} \\\Leftrightarrow &-9x & = &-2\\\Leftrightarrow & \color{red}{-9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+15}& = &-15 \\\Leftrightarrow & x \color{red}{+15}\color{blue}{-15} & = &-15\color{blue}{-15} \\\Leftrightarrow &x & = &-30\\\Leftrightarrow & \color{red}{}x & = &-30\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -30 \\\Leftrightarrow & \color{green}{ x = -30 } & & \\ & V = \left\{ -30 \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-8}& = &1 \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8} & = &1\color{blue}{+8} \\\Leftrightarrow &2x & = &9\\\Leftrightarrow & \color{red}{2}x & = &9\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{9}{2} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+13}& = &12 \\\Leftrightarrow & -3x \color{red}{+13}\color{blue}{-13} & = &12\color{blue}{-13} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-10}& = &1 \\\Leftrightarrow & 9x \color{red}{-10}\color{blue}{+10} & = &1\color{blue}{+10} \\\Leftrightarrow &9x & = &11\\\Leftrightarrow & \color{red}{9}x & = &11\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{11}{9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-13}& = &-4 \\\Leftrightarrow & -5x \color{red}{-13}\color{blue}{+13} & = &-4\color{blue}{+13} \\\Leftrightarrow &-5x & = &9\\\Leftrightarrow & \color{red}{-5}x & = &9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{-6}& = &-2 \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6} & = &-2\color{blue}{+6} \\\Leftrightarrow &-14x & = &4\\\Leftrightarrow & \color{red}{-14}x & = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+2}& = &8 \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2} & = &8\color{blue}{-2} \\\Leftrightarrow &4x & = &6\\\Leftrightarrow & \color{red}{4}x & = &6\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{6}{4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-2}& = &10 \\\Leftrightarrow & 8x \color{red}{-2}\color{blue}{+2} & = &10\color{blue}{+2} \\\Leftrightarrow &8x & = &12\\\Leftrightarrow & \color{red}{8}x & = &12\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{12}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+11}& = &-8 \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11} & = &-8\color{blue}{-11} \\\Leftrightarrow &15x & = &-19\\\Leftrightarrow & \color{red}{15}x & = &-19\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-19}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{15} } & & \\ & V = \left\{ \frac{-19}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+12}& = &-9 \\\Leftrightarrow & -9x \color{red}{+12}\color{blue}{-12} & = &-9\color{blue}{-12} \\\Leftrightarrow &-9x & = &-21\\\Leftrightarrow & \color{red}{-9}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-21}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-14}& = &6 \\\Leftrightarrow & -12x \color{red}{-14}\color{blue}{+14} & = &6\color{blue}{+14} \\\Leftrightarrow &-12x & = &20\\\Leftrightarrow & \color{red}{-12}x & = &20\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{20}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)