Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-5}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-5}\color{blue}{+5-x } & = & -14 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -14 \color{blue}{+5} \\\Leftrightarrow &11x & = &-9\\\Leftrightarrow & \color{red}{11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+13}& = & 1 \color{red}{ +9x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13-9x } & = & 1 \color{red}{ +9x }\color{blue}{-13-9x } \\\Leftrightarrow & 11x \color{blue}{-9x } & = & 1 \color{blue}{-13} \\\Leftrightarrow &2x & = &-12\\\Leftrightarrow & \color{red}{2}x & = &-12\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-12}{2} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+10}& = & -1 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10-10x } & = & -1 \color{red}{ +10x }\color{blue}{-10-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -1 \color{blue}{-10} \\\Leftrightarrow &-19x & = &-11\\\Leftrightarrow & \color{red}{-19}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-11}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{11}{19} } & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+7}& = & 3 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{+7}\color{blue}{-7-12x } & = & 3 \color{red}{ +12x }\color{blue}{-7-12x } \\\Leftrightarrow & -x \color{blue}{-12x } & = & 3 \color{blue}{-7} \\\Leftrightarrow &-13x & = &-4\\\Leftrightarrow & \color{red}{-13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-15}& = & -9 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-15}\color{blue}{+15+11x } & = & -9 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -9 \color{blue}{+15} \\\Leftrightarrow &14x & = &6\\\Leftrightarrow & \color{red}{14}x & = &6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-5}& = & -7 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5-6x } & = & -7 \color{red}{ +6x }\color{blue}{+5-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & -7 \color{blue}{+5} \\\Leftrightarrow &-x & = &-2\\\Leftrightarrow & \color{red}{-}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-2}{-1} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+13}& = & 10 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13-4x } & = & 10 \color{red}{ +4x }\color{blue}{-13-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & 10 \color{blue}{-13} \\\Leftrightarrow &5x & = &-3\\\Leftrightarrow & \color{red}{5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-3}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{-3}\color{blue}{+3-11x } & = & -3 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & -3 \color{blue}{+3} \\\Leftrightarrow &-x & = &0\\\Leftrightarrow & \color{red}{-}x & = &0\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{0}{-1} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-7}& = & 6 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7+8x } & = & 6 \color{red}{ -8x }\color{blue}{+7+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 6 \color{blue}{+7} \\\Leftrightarrow &19x & = &13\\\Leftrightarrow & \color{red}{19}x & = &13\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{13}{19} \\\Leftrightarrow & \color{green}{ x = \frac{13}{19} } & & \\ & V = \left\{ \frac{13}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+1}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1-x } & = & -1 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & -1 \color{blue}{-1} \\\Leftrightarrow &4x & = &-2\\\Leftrightarrow & \color{red}{4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-2}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+13}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+13}\color{blue}{-13-x } & = & -10 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -10 \color{blue}{-13} \\\Leftrightarrow &-15x & = &-23\\\Leftrightarrow & \color{red}{-15}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-23}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{23}{15} } & & \\ & V = \left\{ \frac{23}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-11}& = & 15 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11+5x } & = & 15 \color{red}{ -5x }\color{blue}{+11+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & 15 \color{blue}{+11} \\\Leftrightarrow &16x & = &26\\\Leftrightarrow & \color{red}{16}x & = &26\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{26}{16} \\\Leftrightarrow & \color{green}{ x = \frac{13}{8} } & & \\ & V = \left\{ \frac{13}{8} \right\} & \\\end{align}\)