Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{-12}& = & 4 \color{red}{ +9x } \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12-9x } & = & 4 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & x \color{blue}{-9x } & = & 4 \color{blue}{+12} \\\Leftrightarrow &-8x & = &16\\\Leftrightarrow & \color{red}{-8}x & = &16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{16}{-8} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{-15}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15+11x } & = & -7 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & -7 \color{blue}{+15} \\\Leftrightarrow &20x & = &8\\\Leftrightarrow & \color{red}{20}x & = &8\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{8}{20} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+7}\color{blue}{-7-x } & = & 14 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 14 \color{blue}{-7} \\\Leftrightarrow &-7x & = &7\\\Leftrightarrow & \color{red}{-7}x & = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-14}& = & 13 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14+5x } & = & 13 \color{red}{ -5x }\color{blue}{+14+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & 13 \color{blue}{+14} \\\Leftrightarrow &16x & = &27\\\Leftrightarrow & \color{red}{16}x & = &27\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{27}{16} \\\Leftrightarrow & \color{green}{ x = \frac{27}{16} } & & \\ & V = \left\{ \frac{27}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+14}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14-x } & = & 12 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 12 \color{blue}{-14} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-15}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-x } & = & -13 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -13 \color{blue}{+15} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+5}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5-x } & = & 14 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 14 \color{blue}{-5} \\\Leftrightarrow &-16x & = &9\\\Leftrightarrow & \color{red}{-16}x & = &9\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{9}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{16} } & & \\ & V = \left\{ \frac{-9}{16} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-14}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14-7x } & = & -10 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & 11x \color{blue}{-7x } & = & -10 \color{blue}{+14} \\\Leftrightarrow &4x & = &4\\\Leftrightarrow & \color{red}{4}x & = &4\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{4}{4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+3}& = & -8 \color{red}{ +2x } \\\Leftrightarrow & 7x \color{red}{+3}\color{blue}{-3-2x } & = & -8 \color{red}{ +2x }\color{blue}{-3-2x } \\\Leftrightarrow & 7x \color{blue}{-2x } & = & -8 \color{blue}{-3} \\\Leftrightarrow &5x & = &-11\\\Leftrightarrow & \color{red}{5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-11}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-7}& = & -3 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7-5x } & = & -3 \color{red}{ +5x }\color{blue}{+7-5x } \\\Leftrightarrow & 13x \color{blue}{-5x } & = & -3 \color{blue}{+7} \\\Leftrightarrow &8x & = &4\\\Leftrightarrow & \color{red}{8}x & = &4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+12}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+12}\color{blue}{-12-x } & = & -11 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -11 \color{blue}{-12} \\\Leftrightarrow &-4x & = &-23\\\Leftrightarrow & \color{red}{-4}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-23}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{23}{4} } & & \\ & V = \left\{ \frac{23}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+9}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9+11x } & = & 11 \color{red}{ -11x }\color{blue}{-9+11x } \\\Leftrightarrow & x \color{blue}{+11x } & = & 11 \color{blue}{-9} \\\Leftrightarrow &12x & = &2\\\Leftrightarrow & \color{red}{12}x & = &2\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{2}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)