Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-4}& = & 9 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-4}\color{blue}{+4-10x } & = & 9 \color{red}{ +10x }\color{blue}{+4-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 9 \color{blue}{+4} \\\Leftrightarrow &-13x & = &13\\\Leftrightarrow & \color{red}{-13}x & = &13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{13}{-13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+5}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+5}\color{blue}{-5-x } & = & -14 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -14 \color{blue}{-5} \\\Leftrightarrow &x & = &-19\\\Leftrightarrow & \color{red}{}x & = &-19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -19 \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+13}& = & -8 \color{red}{ -5x } \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13+5x } & = & -8 \color{red}{ -5x }\color{blue}{-13+5x } \\\Leftrightarrow & x \color{blue}{+5x } & = & -8 \color{blue}{-13} \\\Leftrightarrow &6x & = &-21\\\Leftrightarrow & \color{red}{6}x & = &-21\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-21}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{-1}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-x } & = & -5 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -5 \color{blue}{+1} \\\Leftrightarrow &-9x & = &-4\\\Leftrightarrow & \color{red}{-9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{+3}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+3}\color{blue}{-3-x } & = & 5 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 5 \color{blue}{-3} \\\Leftrightarrow &-16x & = &2\\\Leftrightarrow & \color{red}{-16}x & = &2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-12}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-9x } & = & -5 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & -5 \color{blue}{+12} \\\Leftrightarrow &-11x & = &7\\\Leftrightarrow & \color{red}{-11}x & = &7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-8}& = & -2 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8-3x } & = & -2 \color{red}{ +3x }\color{blue}{+8-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & -2 \color{blue}{+8} \\\Leftrightarrow &-14x & = &6\\\Leftrightarrow & \color{red}{-14}x & = &6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{+15}& = & -9 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15+7x } & = & -9 \color{red}{ -7x }\color{blue}{-15+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & -9 \color{blue}{-15} \\\Leftrightarrow &18x & = &-24\\\Leftrightarrow & \color{red}{18}x & = &-24\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{-24}{18} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+4}& = & -2 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4+6x } & = & -2 \color{red}{ -6x }\color{blue}{-4+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &19x & = &-6\\\Leftrightarrow & \color{red}{19}x & = &-6\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-6}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{19} } & & \\ & V = \left\{ \frac{-6}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+13}\color{blue}{-13-x } & = & 4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 4 \color{blue}{-13} \\\Leftrightarrow &x & = &-9\\\Leftrightarrow & \color{red}{}x & = &-9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -9 \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-15}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-15}\color{blue}{+15-x } & = & -5 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -5 \color{blue}{+15} \\\Leftrightarrow &-15x & = &10\\\Leftrightarrow & \color{red}{-15}x & = &10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-2}& = & -2 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2-10x } & = & -2 \color{red}{ +10x }\color{blue}{+2-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & -2 \color{blue}{+2} \\\Leftrightarrow &-x & = &0\\\Leftrightarrow & \color{red}{-}x & = &0\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{0}{-1} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)