Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-13}& = &-13 \\\Leftrightarrow & -x \color{red}{-13}\color{blue}{+13} & = &-13\color{blue}{+13} \\\Leftrightarrow &-x & = &0\\\Leftrightarrow & \color{red}{-}x & = &0\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{0}{-1} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-13}& = &12 \\\Leftrightarrow & -12x \color{red}{-13}\color{blue}{+13} & = &12\color{blue}{+13} \\\Leftrightarrow &-12x & = &25\\\Leftrightarrow & \color{red}{-12}x & = &25\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{25}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{12} } & & \\ & V = \left\{ \frac{-25}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-9}& = &-2 \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9} & = &-2\color{blue}{+9} \\\Leftrightarrow &-3x & = &7\\\Leftrightarrow & \color{red}{-3}x & = &7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{-1}& = &5 \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1} & = &5\color{blue}{+1} \\\Leftrightarrow &-x & = &6\\\Leftrightarrow & \color{red}{-}x & = &6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{6}{-1} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+5}& = &-8 \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5} & = &-8\color{blue}{-5} \\\Leftrightarrow &-13x & = &-13\\\Leftrightarrow & \color{red}{-13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-13}{-13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-7}& = &-9 \\\Leftrightarrow & 7x \color{red}{-7}\color{blue}{+7} & = &-9\color{blue}{+7} \\\Leftrightarrow &7x & = &-2\\\Leftrightarrow & \color{red}{7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+2}& = &15 \\\Leftrightarrow & -4x \color{red}{+2}\color{blue}{-2} & = &15\color{blue}{-2} \\\Leftrightarrow &-4x & = &13\\\Leftrightarrow & \color{red}{-4}x & = &13\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{13}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{4} } & & \\ & V = \left\{ \frac{-13}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-9}& = &3 \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9} & = &3\color{blue}{+9} \\\Leftrightarrow &9x & = &12\\\Leftrightarrow & \color{red}{9}x & = &12\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{12}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-7}& = &-4 \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7} & = &-4\color{blue}{+7} \\\Leftrightarrow &11x & = &3\\\Leftrightarrow & \color{red}{11}x & = &3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-4}& = &-10 \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4} & = &-10\color{blue}{+4} \\\Leftrightarrow &5x & = &-6\\\Leftrightarrow & \color{red}{5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+1}& = &7 \\\Leftrightarrow & -10x \color{red}{+1}\color{blue}{-1} & = &7\color{blue}{-1} \\\Leftrightarrow &-10x & = &6\\\Leftrightarrow & \color{red}{-10}x & = &6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+11}& = &-5 \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11} & = &-5\color{blue}{-11} \\\Leftrightarrow &-8x & = &-16\\\Leftrightarrow & \color{red}{-8}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-16}{-8} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)