Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(6x-3=-2+5x\)
2. \(-9x+14=8+10x\)
3. \(-4x+5=-6+9x\)
4. \(5x-7=2-4x\)
5. \(x-3=15+12x\)
6. \(-x-13=2+0x\)
7. \(-5x+6=15+x\)
8. \(8x-8=9+5x\)
9. \(-4x+3=5+x\)
10. \(6x-10=15-11x\)
11. \(15x+9=-2-14x\)
12. \(-10x-3=-10+x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-3}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3-5x } & = & -2 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+14}& = & 8 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14-10x } & = & 8 \color{red}{ +10x }\color{blue}{-14-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & 8 \color{blue}{-14} \\\Leftrightarrow &-19x & = &-6\\\Leftrightarrow & \color{red}{-19}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-6}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{6}{19} } & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+5}& = & -6 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+5}\color{blue}{-5-9x } & = & -6 \color{red}{ +9x }\color{blue}{-5-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -6 \color{blue}{-5} \\\Leftrightarrow &-13x & = &-11\\\Leftrightarrow & \color{red}{-13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-7}& = & 2 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7+4x } & = & 2 \color{red}{ -4x }\color{blue}{+7+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 2 \color{blue}{+7} \\\Leftrightarrow &9x & = &9\\\Leftrightarrow & \color{red}{9}x & = &9\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{9}{9} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{-3}& = & 15 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3-12x } & = & 15 \color{red}{ +12x }\color{blue}{+3-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & 15 \color{blue}{+3} \\\Leftrightarrow &-11x & = &18\\\Leftrightarrow & \color{red}{-11}x & = &18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-13}& = & 2 \color{red}{ +0x } \\\Leftrightarrow & -x \color{red}{-13}\color{blue}{+13+0x } & = & 2 \color{red}{ +0x }\color{blue}{+13+0x } \\\Leftrightarrow & -x \color{blue}{+0x } & = & 2 \color{blue}{+13} \\\Leftrightarrow &-x & = &15\\\Leftrightarrow & \color{red}{-}x & = &15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{15}{-1} \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+6}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-x } & = & 15 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 15 \color{blue}{-6} \\\Leftrightarrow &-6x & = &9\\\Leftrightarrow & \color{red}{-6}x & = &9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-8}& = & 9 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{-8}\color{blue}{+8-5x } & = & 9 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & 9 \color{blue}{+8} \\\Leftrightarrow &3x & = &17\\\Leftrightarrow & \color{red}{3}x & = &17\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{17}{3} \\\Leftrightarrow & \color{green}{ x = \frac{17}{3} } & & \\ & V = \left\{ \frac{17}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+3}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+3}\color{blue}{-3-x } & = & 5 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 5 \color{blue}{-3} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-10}& = & 15 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-10}\color{blue}{+10+11x } & = & 15 \color{red}{ -11x }\color{blue}{+10+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 15 \color{blue}{+10} \\\Leftrightarrow &17x & = &25\\\Leftrightarrow & \color{red}{17}x & = &25\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{25}{17} \\\Leftrightarrow & \color{green}{ x = \frac{25}{17} } & & \\ & V = \left\{ \frac{25}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+9}& = & -2 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9+14x } & = & -2 \color{red}{ -14x }\color{blue}{-9+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &29x & = &-11\\\Leftrightarrow & \color{red}{29}x & = &-11\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-11}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{29} } & & \\ & V = \left\{ \frac{-11}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-3}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-x } & = & -10 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &-11x & = &-7\\\Leftrightarrow & \color{red}{-11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)