Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-2}& = &2 \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2} & = &2\color{blue}{+2} \\\Leftrightarrow &15x & = &4\\\Leftrightarrow & \color{red}{15}x & = &4\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{4}{15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-12}& = &-7 \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12} & = &-7\color{blue}{+12} \\\Leftrightarrow &12x & = &5\\\Leftrightarrow & \color{red}{12}x & = &5\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{5}{12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+15}& = &-9 \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15} & = &-9\color{blue}{-15} \\\Leftrightarrow &-8x & = &-24\\\Leftrightarrow & \color{red}{-8}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-24}{-8} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+11}& = &9 \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11} & = &9\color{blue}{-11} \\\Leftrightarrow &5x & = &-2\\\Leftrightarrow & \color{red}{5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+5}& = &-6 \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5} & = &-6\color{blue}{-5} \\\Leftrightarrow &-9x & = &-11\\\Leftrightarrow & \color{red}{-9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{+11}& = &13 \\\Leftrightarrow & -7x \color{red}{+11}\color{blue}{-11} & = &13\color{blue}{-11} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-10}& = &-12 \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10} & = &-12\color{blue}{+10} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+9}& = &6 \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9} & = &6\color{blue}{-9} \\\Leftrightarrow &-13x & = &-3\\\Leftrightarrow & \color{red}{-13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+13}& = &-14 \\\Leftrightarrow & -x \color{red}{+13}\color{blue}{-13} & = &-14\color{blue}{-13} \\\Leftrightarrow &-x & = &-27\\\Leftrightarrow & \color{red}{-}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-27}{-1} \\\Leftrightarrow & \color{green}{ x = 27 } & & \\ & V = \left\{ 27 \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-10}& = &-10 \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10} & = &-10\color{blue}{+10} \\\Leftrightarrow &12x & = &0\\\Leftrightarrow & \color{red}{12}x & = &0\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{0}{12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+9}& = &6 \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9} & = &6\color{blue}{-9} \\\Leftrightarrow &6x & = &-3\\\Leftrightarrow & \color{red}{6}x & = &-3\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-3}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{+10}& = &12 \\\Leftrightarrow & -12x \color{red}{+10}\color{blue}{-10} & = &12\color{blue}{-10} \\\Leftrightarrow &-12x & = &2\\\Leftrightarrow & \color{red}{-12}x & = &2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)