Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-8}& = & 12 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8-8x } & = & 12 \color{red}{ +8x }\color{blue}{+8-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & 12 \color{blue}{+8} \\\Leftrightarrow &-13x & = &20\\\Leftrightarrow & \color{red}{-13}x & = &20\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{20}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{13} } & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-8}& = & -12 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8+11x } & = & -12 \color{red}{ -11x }\color{blue}{+8+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & -12 \color{blue}{+8} \\\Leftrightarrow &25x & = &-4\\\Leftrightarrow & \color{red}{25}x & = &-4\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-4}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{25} } & & \\ & V = \left\{ \frac{-4}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-14}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14-13x } & = & 2 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & 2 \color{blue}{+14} \\\Leftrightarrow &-7x & = &16\\\Leftrightarrow & \color{red}{-7}x & = &16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{7} } & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+4}& = & -10 \color{red}{ +8x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-8x } & = & -10 \color{red}{ +8x }\color{blue}{-4-8x } \\\Leftrightarrow & -13x \color{blue}{-8x } & = & -10 \color{blue}{-4} \\\Leftrightarrow &-21x & = &-14\\\Leftrightarrow & \color{red}{-21}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-14}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-9}& = & -12 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9-3x } & = & -12 \color{red}{ +3x }\color{blue}{+9-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & -12 \color{blue}{+9} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+5}& = & -6 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{+5}\color{blue}{-5+11x } & = & -6 \color{red}{ -11x }\color{blue}{-5+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & -6 \color{blue}{-5} \\\Leftrightarrow &20x & = &-11\\\Leftrightarrow & \color{red}{20}x & = &-11\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-11}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{20} } & & \\ & V = \left\{ \frac{-11}{20} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-3}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3-x } & = & -12 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -12 \color{blue}{+3} \\\Leftrightarrow &13x & = &-9\\\Leftrightarrow & \color{red}{13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-12}& = & -15 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-8x } & = & -15 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -15 \color{blue}{+12} \\\Leftrightarrow &-23x & = &-3\\\Leftrightarrow & \color{red}{-23}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-3}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{3}{23} } & & \\ & V = \left\{ \frac{3}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+2}& = & 8 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2-11x } & = & 8 \color{red}{ +11x }\color{blue}{-2-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 8 \color{blue}{-2} \\\Leftrightarrow &-5x & = &6\\\Leftrightarrow & \color{red}{-5}x & = &6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+5}& = & -3 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-6x } & = & -3 \color{red}{ +6x }\color{blue}{-5-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &-11x & = &-8\\\Leftrightarrow & \color{red}{-11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+15}& = & -2 \color{red}{ -13x } \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15+13x } & = & -2 \color{red}{ -13x }\color{blue}{-15+13x } \\\Leftrightarrow & -x \color{blue}{+13x } & = & -2 \color{blue}{-15} \\\Leftrightarrow &12x & = &-17\\\Leftrightarrow & \color{red}{12}x & = &-17\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-17}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{12} } & & \\ & V = \left\{ \frac{-17}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-10}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-10}\color{blue}{+10-x } & = & 9 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 9 \color{blue}{+10} \\\Leftrightarrow &7x & = &19\\\Leftrightarrow & \color{red}{7}x & = &19\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{19}{7} \\\Leftrightarrow & \color{green}{ x = \frac{19}{7} } & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)