Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-2}& = & 6 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-2}\color{blue}{+2+7x } & = & 6 \color{red}{ -7x }\color{blue}{+2+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 6 \color{blue}{+2} \\\Leftrightarrow &15x & = &8\\\Leftrightarrow & \color{red}{15}x & = &8\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{8}{15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+11}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+11}\color{blue}{-11-x } & = & -14 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &9x & = &-25\\\Leftrightarrow & \color{red}{9}x & = &-25\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-25}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{9} } & & \\ & V = \left\{ \frac{-25}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-9}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-x } & = & -10 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+13}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13-x } & = & -10 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -10 \color{blue}{-13} \\\Leftrightarrow &5x & = &-23\\\Leftrightarrow & \color{red}{5}x & = &-23\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-23}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{5} } & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+14}& = & 12 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14+2x } & = & 12 \color{red}{ -2x }\color{blue}{-14+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & 12 \color{blue}{-14} \\\Leftrightarrow &5x & = &-2\\\Leftrightarrow & \color{red}{5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-12}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12-9x } & = & 8 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 8 \color{blue}{+12} \\\Leftrightarrow &-17x & = &20\\\Leftrightarrow & \color{red}{-17}x & = &20\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{20}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{17} } & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+13}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{+13}\color{blue}{-13-5x } & = & -4 \color{red}{ +5x }\color{blue}{-13-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & -4 \color{blue}{-13} \\\Leftrightarrow &-19x & = &-17\\\Leftrightarrow & \color{red}{-19}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-17}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{17}{19} } & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+15}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15-9x } & = & -14 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & -14 \color{blue}{-15} \\\Leftrightarrow &-x & = &-29\\\Leftrightarrow & \color{red}{-}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-29}{-1} \\\Leftrightarrow & \color{green}{ x = 29 } & & \\ & V = \left\{ 29 \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{+7}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+7}\color{blue}{-7-x } & = & -14 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -14 \color{blue}{-7} \\\Leftrightarrow &-10x & = &-21\\\Leftrightarrow & \color{red}{-10}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-21}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{21}{10} } & & \\ & V = \left\{ \frac{21}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-5}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-x } & = & -6 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -6 \color{blue}{+5} \\\Leftrightarrow &x & = &-1\\\Leftrightarrow & \color{red}{}x & = &-1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -1 \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-10}& = & -8 \color{red}{ -15x } \\\Leftrightarrow & x \color{red}{-10}\color{blue}{+10+15x } & = & -8 \color{red}{ -15x }\color{blue}{+10+15x } \\\Leftrightarrow & x \color{blue}{+15x } & = & -8 \color{blue}{+10} \\\Leftrightarrow &16x & = &2\\\Leftrightarrow & \color{red}{16}x & = &2\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{2}{16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+5}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-x } & = & -3 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &-3x & = &-8\\\Leftrightarrow & \color{red}{-3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)