Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+12}& = & 13 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12-3x } & = & 13 \color{red}{ +3x }\color{blue}{-12-3x } \\\Leftrightarrow & -8x \color{blue}{-3x } & = & 13 \color{blue}{-12} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-3}& = & 4 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3-5x } & = & 4 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & 4 \color{blue}{+3} \\\Leftrightarrow &9x & = &7\\\Leftrightarrow & \color{red}{9}x & = &7\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{7}{9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-15}& = & -13 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15+13x } & = & -13 \color{red}{ -13x }\color{blue}{+15+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -13 \color{blue}{+15} \\\Leftrightarrow &24x & = &2\\\Leftrightarrow & \color{red}{24}x & = &2\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{2}{24} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-5}& = & -8 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-5}\color{blue}{+5+9x } & = & -8 \color{red}{ -9x }\color{blue}{+5+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -8 \color{blue}{+5} \\\Leftrightarrow &19x & = &-3\\\Leftrightarrow & \color{red}{19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-3}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{19} } & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+6}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6-7x } & = & -12 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -12 \color{blue}{-6} \\\Leftrightarrow &3x & = &-18\\\Leftrightarrow & \color{red}{3}x & = &-18\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-18}{3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+3}& = & 2 \color{red}{ +3x } \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3-3x } & = & 2 \color{red}{ +3x }\color{blue}{-3-3x } \\\Leftrightarrow & 11x \color{blue}{-3x } & = & 2 \color{blue}{-3} \\\Leftrightarrow &8x & = &-1\\\Leftrightarrow & \color{red}{8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+4}& = & 15 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4+15x } & = & 15 \color{red}{ -15x }\color{blue}{-4+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 15 \color{blue}{-4} \\\Leftrightarrow &23x & = &11\\\Leftrightarrow & \color{red}{23}x & = &11\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{11}{23} \\\Leftrightarrow & \color{green}{ x = \frac{11}{23} } & & \\ & V = \left\{ \frac{11}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-11}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11-x } & = & -11 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -11 \color{blue}{+11} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+5}& = & -3 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-12x } & = & -3 \color{red}{ +12x }\color{blue}{-5-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &-23x & = &-8\\\Leftrightarrow & \color{red}{-23}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-8}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{8}{23} } & & \\ & V = \left\{ \frac{8}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-8}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8-x } & = & -8 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -8 \color{blue}{+8} \\\Leftrightarrow &-5x & = &0\\\Leftrightarrow & \color{red}{-5}x & = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14-x } & = & 4 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 4 \color{blue}{+14} \\\Leftrightarrow &-4x & = &18\\\Leftrightarrow & \color{red}{-4}x & = &18\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{18}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-11}& = & -7 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11+4x } & = & -7 \color{red}{ -4x }\color{blue}{+11+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -7 \color{blue}{+11} \\\Leftrightarrow &13x & = &4\\\Leftrightarrow & \color{red}{13}x & = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)