Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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