Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(-x+15=9-12x\)
2. \(x+4=-3+0x\)
3. \(6x-15=-12+5x\)
4. \(5x-8=-4-12x\)
5. \(15x-2=-10-14x\)
6. \(6x-4=-8+7x\)
7. \(12x+7=13+x\)
8. \(5x+13=-5-14x\)
9. \(-11x-1=-2+12x\)
10. \(9x+1=-14-4x\)
11. \(15x+5=9+x\)
12. \(9x-11=-4-8x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+15}& = & 9 \color{red}{ -12x } \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15+12x } & = & 9 \color{red}{ -12x }\color{blue}{-15+12x } \\\Leftrightarrow & -x \color{blue}{+12x } & = & 9 \color{blue}{-15} \\\Leftrightarrow &11x & = &-6\\\Leftrightarrow & \color{red}{11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+4}& = & -3 \color{red}{ +0x } \\\Leftrightarrow & x \color{red}{+4}\color{blue}{-4+0x } & = & -3 \color{red}{ +0x }\color{blue}{-4+0x } \\\Leftrightarrow & x \color{blue}{+0x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &x & = &-7\\\Leftrightarrow & \color{red}{}x & = &-7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -7 \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-15}& = & -12 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15-5x } & = & -12 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -12 \color{blue}{+15} \\\Leftrightarrow &x & = &3\\\Leftrightarrow & \color{red}{}x & = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-8}& = & -4 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8+12x } & = & -4 \color{red}{ -12x }\color{blue}{+8+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & -4 \color{blue}{+8} \\\Leftrightarrow &17x & = &4\\\Leftrightarrow & \color{red}{17}x & = &4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{-2}& = & -10 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2+14x } & = & -10 \color{red}{ -14x }\color{blue}{+2+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & -10 \color{blue}{+2} \\\Leftrightarrow &29x & = &-8\\\Leftrightarrow & \color{red}{29}x & = &-8\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-8}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{29} } & & \\ & V = \left\{ \frac{-8}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-4}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4-7x } & = & -8 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & -8 \color{blue}{+4} \\\Leftrightarrow &-x & = &-4\\\Leftrightarrow & \color{red}{-}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-4}{-1} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+7}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7-x } & = & 13 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 13 \color{blue}{-7} \\\Leftrightarrow &11x & = &6\\\Leftrightarrow & \color{red}{11}x & = &6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+13}& = & -5 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{+13}\color{blue}{-13+14x } & = & -5 \color{red}{ -14x }\color{blue}{-13+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -5 \color{blue}{-13} \\\Leftrightarrow &19x & = &-18\\\Leftrightarrow & \color{red}{19}x & = &-18\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-18}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{19} } & & \\ & V = \left\{ \frac{-18}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-1}& = & -2 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1-12x } & = & -2 \color{red}{ +12x }\color{blue}{+1-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & -2 \color{blue}{+1} \\\Leftrightarrow &-23x & = &-1\\\Leftrightarrow & \color{red}{-23}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-1}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{1}{23} } & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+1}& = & -14 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1+4x } & = & -14 \color{red}{ -4x }\color{blue}{-1+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -14 \color{blue}{-1} \\\Leftrightarrow &13x & = &-15\\\Leftrightarrow & \color{red}{13}x & = &-15\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-15}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{13} } & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+5}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{+5}\color{blue}{-5-x } & = & 9 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & 9 \color{blue}{-5} \\\Leftrightarrow &14x & = &4\\\Leftrightarrow & \color{red}{14}x & = &4\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{4}{14} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-11}& = & -4 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11+8x } & = & -4 \color{red}{ -8x }\color{blue}{+11+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -4 \color{blue}{+11} \\\Leftrightarrow &17x & = &7\\\Leftrightarrow & \color{red}{17}x & = &7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)