Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+2}& = & -8 \color{red}{ +8x } \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2-8x } & = & -8 \color{red}{ +8x }\color{blue}{-2-8x } \\\Leftrightarrow & 11x \color{blue}{-8x } & = & -8 \color{blue}{-2} \\\Leftrightarrow &3x & = &-10\\\Leftrightarrow & \color{red}{3}x & = &-10\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-10}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{+5}& = & -8 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5+11x } & = & -8 \color{red}{ -11x }\color{blue}{-5+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -8 \color{blue}{-5} \\\Leftrightarrow &14x & = &-13\\\Leftrightarrow & \color{red}{14}x & = &-13\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-13}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{14} } & & \\ & V = \left\{ \frac{-13}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-5}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5-x } & = & 4 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 4 \color{blue}{+5} \\\Leftrightarrow &4x & = &9\\\Leftrightarrow & \color{red}{4}x & = &9\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{9}{4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{+11}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+11}\color{blue}{-11-x } & = & -13 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -13 \color{blue}{-11} \\\Leftrightarrow &-15x & = &-24\\\Leftrightarrow & \color{red}{-15}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-24}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+11}& = & -8 \color{red}{ +4x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11-4x } & = & -8 \color{red}{ +4x }\color{blue}{-11-4x } \\\Leftrightarrow & 13x \color{blue}{-4x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &9x & = &-19\\\Leftrightarrow & \color{red}{9}x & = &-19\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-19}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{9} } & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-2}& = & -9 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2+6x } & = & -9 \color{red}{ -6x }\color{blue}{+2+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -9 \color{blue}{+2} \\\Leftrightarrow &19x & = &-7\\\Leftrightarrow & \color{red}{19}x & = &-7\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-7}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{19} } & & \\ & V = \left\{ \frac{-7}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-9}& = & 7 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9-9x } & = & 7 \color{red}{ +9x }\color{blue}{+9-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 7 \color{blue}{+9} \\\Leftrightarrow &-13x & = &16\\\Leftrightarrow & \color{red}{-13}x & = &16\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{16}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{13} } & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+13}& = & 15 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+13}\color{blue}{-13+3x } & = & 15 \color{red}{ -3x }\color{blue}{-13+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &7x & = &2\\\Leftrightarrow & \color{red}{7}x & = &2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-12}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-x } & = & 13 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 13 \color{blue}{+12} \\\Leftrightarrow &-3x & = &25\\\Leftrightarrow & \color{red}{-3}x & = &25\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{25}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{3} } & & \\ & V = \left\{ \frac{-25}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-1}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{-1}\color{blue}{+1+7x } & = & 2 \color{red}{ -7x }\color{blue}{+1+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &18x & = &3\\\Leftrightarrow & \color{red}{18}x & = &3\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{3}{18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{+15}& = & -6 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15-9x } & = & -6 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -6 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-21\\\Leftrightarrow & \color{red}{-5}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-21}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{21}{5} } & & \\ & V = \left\{ \frac{21}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-8}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-8}\color{blue}{+8-5x } & = & 2 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 2 \color{blue}{+8} \\\Leftrightarrow &x & = &10\\\Leftrightarrow & \color{red}{}x & = &10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 10 \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)