Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-10}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10-x } & = & 12 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 12 \color{blue}{+10} \\\Leftrightarrow &-6x & = &22\\\Leftrightarrow & \color{red}{-6}x & = &22\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{22}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+6}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-x } & = & 2 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 2 \color{blue}{-6} \\\Leftrightarrow &-16x & = &-4\\\Leftrightarrow & \color{red}{-16}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-14}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14-x } & = & -10 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -10 \color{blue}{+14} \\\Leftrightarrow &-3x & = &4\\\Leftrightarrow & \color{red}{-3}x & = &4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+1}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & -13x \color{red}{+1}\color{blue}{-1-11x } & = & -8 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & -13x \color{blue}{-11x } & = & -8 \color{blue}{-1} \\\Leftrightarrow &-24x & = &-9\\\Leftrightarrow & \color{red}{-24}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-24}x}{ \color{blue}{ -24}} & = & \frac{-9}{-24} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-10}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-5x } & = & 15 \color{red}{ +5x }\color{blue}{+10-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 15 \color{blue}{+10} \\\Leftrightarrow &-17x & = &25\\\Leftrightarrow & \color{red}{-17}x & = &25\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{25}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{17} } & & \\ & V = \left\{ \frac{-25}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{+7}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+7}\color{blue}{-7-13x } & = & -12 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &-17x & = &-19\\\Leftrightarrow & \color{red}{-17}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-19}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{19}{17} } & & \\ & V = \left\{ \frac{19}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{-8}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-8}\color{blue}{+8-x } & = & -13 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &-13x & = &-5\\\Leftrightarrow & \color{red}{-13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{+5}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+5}\color{blue}{-5-13x } & = & 9 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 9 \color{blue}{-5} \\\Leftrightarrow &-19x & = &4\\\Leftrightarrow & \color{red}{-19}x & = &4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-1}& = & 9 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-1}\color{blue}{+1+3x } & = & 9 \color{red}{ -3x }\color{blue}{+1+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &10x & = &10\\\Leftrightarrow & \color{red}{10}x & = &10\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{10}{10} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{-2}& = & 3 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-8x } & = & 3 \color{red}{ +8x }\color{blue}{+2-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & 3 \color{blue}{+2} \\\Leftrightarrow &-23x & = &5\\\Leftrightarrow & \color{red}{-23}x & = &5\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{5}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{23} } & & \\ & V = \left\{ \frac{-5}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{-4}& = & 8 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-4}\color{blue}{+4+4x } & = & 8 \color{red}{ -4x }\color{blue}{+4+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &13x & = &12\\\Leftrightarrow & \color{red}{13}x & = &12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+14}& = & -14 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{+14}\color{blue}{-14-3x } & = & -14 \color{red}{ +3x }\color{blue}{-14-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & -14 \color{blue}{-14} \\\Leftrightarrow &-17x & = &-28\\\Leftrightarrow & \color{red}{-17}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-28}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{28}{17} } & & \\ & V = \left\{ \frac{28}{17} \right\} & \\\end{align}\)