Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{-6}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-x } & = & 1 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 1 \color{blue}{+6} \\\Leftrightarrow &-5x & = &7\\\Leftrightarrow & \color{red}{-5}x & = &7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+1}& = & 13 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1+7x } & = & 13 \color{red}{ -7x }\color{blue}{-1+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &15x & = &12\\\Leftrightarrow & \color{red}{15}x & = &12\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{12}{15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+1}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+1}\color{blue}{-1-x } & = & 14 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 14 \color{blue}{-1} \\\Leftrightarrow &-14x & = &13\\\Leftrightarrow & \color{red}{-14}x & = &13\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{13}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{14} } & & \\ & V = \left\{ \frac{-13}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{+3}& = & -6 \color{red}{ +15x } \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3-15x } & = & -6 \color{red}{ +15x }\color{blue}{-3-15x } \\\Leftrightarrow & x \color{blue}{-15x } & = & -6 \color{blue}{-3} \\\Leftrightarrow &-14x & = &-9\\\Leftrightarrow & \color{red}{-14}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-12}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-12}\color{blue}{+12-x } & = & 11 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 11 \color{blue}{+12} \\\Leftrightarrow &-12x & = &23\\\Leftrightarrow & \color{red}{-12}x & = &23\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{23}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{12} } & & \\ & V = \left\{ \frac{-23}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-13}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13-13x } & = & -4 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & -4 \color{blue}{+13} \\\Leftrightarrow &-7x & = &9\\\Leftrightarrow & \color{red}{-7}x & = &9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-1}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-1}\color{blue}{+1-7x } & = & 2 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+3}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3-x } & = & 4 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 4 \color{blue}{-3} \\\Leftrightarrow &-12x & = &1\\\Leftrightarrow & \color{red}{-12}x & = &1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+5}& = & 8 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{+5}\color{blue}{-5+5x } & = & 8 \color{red}{ -5x }\color{blue}{-5+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & 8 \color{blue}{-5} \\\Leftrightarrow &16x & = &3\\\Leftrightarrow & \color{red}{16}x & = &3\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{3}{16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{16} } & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-8}& = & 1 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8-11x } & = & 1 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &-7x & = &9\\\Leftrightarrow & \color{red}{-7}x & = &9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-6}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-x } & = & -5 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -5 \color{blue}{+6} \\\Leftrightarrow &-15x & = &1\\\Leftrightarrow & \color{red}{-15}x & = &1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-5}& = & 4 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-5}\color{blue}{+5+6x } & = & 4 \color{red}{ -6x }\color{blue}{+5+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 4 \color{blue}{+5} \\\Leftrightarrow &19x & = &9\\\Leftrightarrow & \color{red}{19}x & = &9\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{9}{19} \\\Leftrightarrow & \color{green}{ x = \frac{9}{19} } & & \\ & V = \left\{ \frac{9}{19} \right\} & \\\end{align}\)