Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-14}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14-5x } & = & 15 \color{red}{ +5x }\color{blue}{+14-5x } \\\Leftrightarrow & 13x \color{blue}{-5x } & = & 15 \color{blue}{+14} \\\Leftrightarrow &8x & = &29\\\Leftrightarrow & \color{red}{8}x & = &29\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{29}{8} \\\Leftrightarrow & \color{green}{ x = \frac{29}{8} } & & \\ & V = \left\{ \frac{29}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{-15}& = & -8 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{-15}\color{blue}{+15-8x } & = & -8 \color{red}{ +8x }\color{blue}{+15-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & -8 \color{blue}{+15} \\\Leftrightarrow &-3x & = &7\\\Leftrightarrow & \color{red}{-3}x & = &7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+2}& = & 1 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2+2x } & = & 1 \color{red}{ -2x }\color{blue}{-2+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & 1 \color{blue}{-2} \\\Leftrightarrow &7x & = &-1\\\Leftrightarrow & \color{red}{7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+13}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-x } & = & 6 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 6 \color{blue}{-13} \\\Leftrightarrow &-13x & = &-7\\\Leftrightarrow & \color{red}{-13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-x } & = & 4 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 4 \color{blue}{+2} \\\Leftrightarrow &-16x & = &6\\\Leftrightarrow & \color{red}{-16}x & = &6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-2}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-2}\color{blue}{+2-x } & = & 12 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 12 \color{blue}{+2} \\\Leftrightarrow &-5x & = &14\\\Leftrightarrow & \color{red}{-5}x & = &14\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{14}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{5} } & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+4}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4-x } & = & -15 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -15 \color{blue}{-4} \\\Leftrightarrow &-15x & = &-19\\\Leftrightarrow & \color{red}{-15}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-19}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{19}{15} } & & \\ & V = \left\{ \frac{19}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-12}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12-7x } & = & 12 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &-16x & = &24\\\Leftrightarrow & \color{red}{-16}x & = &24\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{24}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+2}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-x } & = & -1 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -1 \color{blue}{-2} \\\Leftrightarrow &13x & = &-3\\\Leftrightarrow & \color{red}{13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{+11}& = & 2 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+11}\color{blue}{-11-4x } & = & 2 \color{red}{ +4x }\color{blue}{-11-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &-7x & = &-9\\\Leftrightarrow & \color{red}{-7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-6}& = & 5 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6+7x } & = & 5 \color{red}{ -7x }\color{blue}{+6+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 5 \color{blue}{+6} \\\Leftrightarrow &11x & = &11\\\Leftrightarrow & \color{red}{11}x & = &11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{11}{11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{+2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-x } & = & -3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &-4x & = &-5\\\Leftrightarrow & \color{red}{-4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)