Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+4}& = &10 \\\Leftrightarrow & -3x \color{red}{+4}\color{blue}{-4} & = &10\color{blue}{-4} \\\Leftrightarrow &-3x & = &6\\\Leftrightarrow & \color{red}{-3}x & = &6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{6}{-3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-13}& = &-1 \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13} & = &-1\color{blue}{+13} \\\Leftrightarrow &-8x & = &12\\\Leftrightarrow & \color{red}{-8}x & = &12\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{12}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-8}& = &2 \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8} & = &2\color{blue}{+8} \\\Leftrightarrow &9x & = &10\\\Leftrightarrow & \color{red}{9}x & = &10\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{10}{9} \\\Leftrightarrow & \color{green}{ x = \frac{10}{9} } & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-15}& = &4 \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15} & = &4\color{blue}{+15} \\\Leftrightarrow &14x & = &19\\\Leftrightarrow & \color{red}{14}x & = &19\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{19}{14} \\\Leftrightarrow & \color{green}{ x = \frac{19}{14} } & & \\ & V = \left\{ \frac{19}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{+10}& = &-12 \\\Leftrightarrow & -10x \color{red}{+10}\color{blue}{-10} & = &-12\color{blue}{-10} \\\Leftrightarrow &-10x & = &-22\\\Leftrightarrow & \color{red}{-10}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-22}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{+8}& = &3 \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8} & = &3\color{blue}{-8} \\\Leftrightarrow &-6x & = &-5\\\Leftrightarrow & \color{red}{-6}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+8}& = &14 \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8} & = &14\color{blue}{-8} \\\Leftrightarrow &-4x & = &6\\\Leftrightarrow & \color{red}{-4}x & = &6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+4}& = &4 \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4} & = &4\color{blue}{-4} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-8}& = &-4 \\\Leftrightarrow & -10x \color{red}{-8}\color{blue}{+8} & = &-4\color{blue}{+8} \\\Leftrightarrow &-10x & = &4\\\Leftrightarrow & \color{red}{-10}x & = &4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-2}& = &-6 \\\Leftrightarrow & -x \color{red}{-2}\color{blue}{+2} & = &-6\color{blue}{+2} \\\Leftrightarrow &-x & = &-4\\\Leftrightarrow & \color{red}{-}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-4}{-1} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+5}& = &9 \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5} & = &9\color{blue}{-5} \\\Leftrightarrow &-10x & = &4\\\Leftrightarrow & \color{red}{-10}x & = &4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-14}& = &2 \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14} & = &2\color{blue}{+14} \\\Leftrightarrow &-14x & = &16\\\Leftrightarrow & \color{red}{-14}x & = &16\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{16}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)