Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+12}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+12}\color{blue}{-12-5x } & = & -9 \color{red}{ +5x }\color{blue}{-12-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -9 \color{blue}{-12} \\\Leftrightarrow &-14x & = &-21\\\Leftrightarrow & \color{red}{-14}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-21}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-9}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-9}\color{blue}{+9-x } & = & 2 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 2 \color{blue}{+9} \\\Leftrightarrow &5x & = &11\\\Leftrightarrow & \color{red}{5}x & = &11\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{11}{5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-14}& = & 3 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14+7x } & = & 3 \color{red}{ -7x }\color{blue}{+14+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 3 \color{blue}{+14} \\\Leftrightarrow &19x & = &17\\\Leftrightarrow & \color{red}{19}x & = &17\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{17}{19} \\\Leftrightarrow & \color{green}{ x = \frac{17}{19} } & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+11}& = & -8 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11+9x } & = & -8 \color{red}{ -9x }\color{blue}{-11+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &14x & = &-19\\\Leftrightarrow & \color{red}{14}x & = &-19\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-19}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{14} } & & \\ & V = \left\{ \frac{-19}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+7}& = & 14 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7+2x } & = & 14 \color{red}{ -2x }\color{blue}{-7+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 14 \color{blue}{-7} \\\Leftrightarrow &17x & = &7\\\Leftrightarrow & \color{red}{17}x & = &7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+1}& = & -8 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1-9x } & = & -8 \color{red}{ +9x }\color{blue}{-1-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -8 \color{blue}{-1} \\\Leftrightarrow &-17x & = &-9\\\Leftrightarrow & \color{red}{-17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-9}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+9}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-x } & = & 7 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 7 \color{blue}{-9} \\\Leftrightarrow &-16x & = &-2\\\Leftrightarrow & \color{red}{-16}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{+1}& = & 5 \color{red}{ +10x } \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1-10x } & = & 5 \color{red}{ +10x }\color{blue}{-1-10x } \\\Leftrightarrow & -x \color{blue}{-10x } & = & 5 \color{blue}{-1} \\\Leftrightarrow &-11x & = &4\\\Leftrightarrow & \color{red}{-11}x & = &4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+14}& = & -4 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-14x } & = & -4 \color{red}{ +14x }\color{blue}{-14-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &-27x & = &-18\\\Leftrightarrow & \color{red}{-27}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-18}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-11}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{-11}\color{blue}{+11-5x } & = & 15 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & 15 \color{blue}{+11} \\\Leftrightarrow &9x & = &26\\\Leftrightarrow & \color{red}{9}x & = &26\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{26}{9} \\\Leftrightarrow & \color{green}{ x = \frac{26}{9} } & & \\ & V = \left\{ \frac{26}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-1}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & -7 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -7 \color{blue}{+1} \\\Leftrightarrow &-15x & = &-6\\\Leftrightarrow & \color{red}{-15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+2}& = & -15 \color{red}{ +2x } \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2-2x } & = & -15 \color{red}{ +2x }\color{blue}{-2-2x } \\\Leftrightarrow & 11x \color{blue}{-2x } & = & -15 \color{blue}{-2} \\\Leftrightarrow &9x & = &-17\\\Leftrightarrow & \color{red}{9}x & = &-17\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-17}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{9} } & & \\ & V = \left\{ \frac{-17}{9} \right\} & \\\end{align}\)