Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-6}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6-x } & = & -10 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -10 \color{blue}{+6} \\\Leftrightarrow &-14x & = &-4\\\Leftrightarrow & \color{red}{-14}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-9}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9-7x } & = & 10 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &-17x & = &19\\\Leftrightarrow & \color{red}{-17}x & = &19\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{19}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{17} } & & \\ & V = \left\{ \frac{-19}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-7}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-x } & = & 9 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 9 \color{blue}{+7} \\\Leftrightarrow &-14x & = &16\\\Leftrightarrow & \color{red}{-14}x & = &16\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{16}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-8}& = & 1 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8-9x } & = & 1 \color{red}{ +9x }\color{blue}{+8-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &-7x & = &9\\\Leftrightarrow & \color{red}{-7}x & = &9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-15}& = & -6 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-9x } & = & -6 \color{red}{ +9x }\color{blue}{+15-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & -6 \color{blue}{+15} \\\Leftrightarrow &-20x & = &9\\\Leftrightarrow & \color{red}{-20}x & = &9\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{9}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{20} } & & \\ & V = \left\{ \frac{-9}{20} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{-8}& = & 13 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-8}\color{blue}{+8+14x } & = & 13 \color{red}{ -14x }\color{blue}{+8+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & 13 \color{blue}{+8} \\\Leftrightarrow &17x & = &21\\\Leftrightarrow & \color{red}{17}x & = &21\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{21}{17} \\\Leftrightarrow & \color{green}{ x = \frac{21}{17} } & & \\ & V = \left\{ \frac{21}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{-3}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-3}\color{blue}{+3-x } & = & 15 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 15 \color{blue}{+3} \\\Leftrightarrow &-15x & = &18\\\Leftrightarrow & \color{red}{-15}x & = &18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-10}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-10}\color{blue}{+10-x } & = & 4 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 4 \color{blue}{+10} \\\Leftrightarrow &-16x & = &14\\\Leftrightarrow & \color{red}{-16}x & = &14\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{14}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-8}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8-13x } & = & -10 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & -10 \color{blue}{+8} \\\Leftrightarrow &-11x & = &-2\\\Leftrightarrow & \color{red}{-11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+11}& = & 14 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11-14x } & = & 14 \color{red}{ +14x }\color{blue}{-11-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 14 \color{blue}{-11} \\\Leftrightarrow &-23x & = &3\\\Leftrightarrow & \color{red}{-23}x & = &3\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{3}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{23} } & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{+12}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+12}\color{blue}{-12-9x } & = & 3 \color{red}{ +9x }\color{blue}{-12-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 3 \color{blue}{-12} \\\Leftrightarrow &5x & = &-9\\\Leftrightarrow & \color{red}{5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+12}& = & -6 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+12}\color{blue}{-12+14x } & = & -6 \color{red}{ -14x }\color{blue}{-12+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & -6 \color{blue}{-12} \\\Leftrightarrow &29x & = &-18\\\Leftrightarrow & \color{red}{29}x & = &-18\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-18}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{29} } & & \\ & V = \left\{ \frac{-18}{29} \right\} & \\\end{align}\)