Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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