Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-15}& = & -1 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-15}\color{blue}{+15+8x } & = & -1 \color{red}{ -8x }\color{blue}{+15+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -1 \color{blue}{+15} \\\Leftrightarrow &11x & = &14\\\Leftrightarrow & \color{red}{11}x & = &14\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{14}{11} \\\Leftrightarrow & \color{green}{ x = \frac{14}{11} } & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-12}& = & -15 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12+5x } & = & -15 \color{red}{ -5x }\color{blue}{+12+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -15 \color{blue}{+12} \\\Leftrightarrow &11x & = &-3\\\Leftrightarrow & \color{red}{11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+3}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+3}\color{blue}{-3-x } & = & -1 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -1 \color{blue}{-3} \\\Leftrightarrow &-3x & = &-4\\\Leftrightarrow & \color{red}{-3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-12}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-13x } & = & 6 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 6 \color{blue}{+12} \\\Leftrightarrow &-19x & = &18\\\Leftrightarrow & \color{red}{-19}x & = &18\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{18}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{19} } & & \\ & V = \left\{ \frac{-18}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+2}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+2}\color{blue}{-2-x } & = & 9 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 9 \color{blue}{-2} \\\Leftrightarrow &-3x & = &7\\\Leftrightarrow & \color{red}{-3}x & = &7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+7}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7-x } & = & -15 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -15 \color{blue}{-7} \\\Leftrightarrow &-6x & = &-22\\\Leftrightarrow & \color{red}{-6}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-22}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-1}& = & -2 \color{red}{ +0x } \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1+0x } & = & -2 \color{red}{ +0x }\color{blue}{+1+0x } \\\Leftrightarrow & x \color{blue}{+0x } & = & -2 \color{blue}{+1} \\\Leftrightarrow &x & = &-1\\\Leftrightarrow & \color{red}{}x & = &-1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -1 \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+13}& = & -2 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{+13}\color{blue}{-13+12x } & = & -2 \color{red}{ -12x }\color{blue}{-13+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & -2 \color{blue}{-13} \\\Leftrightarrow &17x & = &-15\\\Leftrightarrow & \color{red}{17}x & = &-15\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-15}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{17} } & & \\ & V = \left\{ \frac{-15}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-10}& = & 14 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10-3x } & = & 14 \color{red}{ +3x }\color{blue}{+10-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & 14 \color{blue}{+10} \\\Leftrightarrow &-17x & = &24\\\Leftrightarrow & \color{red}{-17}x & = &24\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{24}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{17} } & & \\ & V = \left\{ \frac{-24}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+5}& = & -3 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5+7x } & = & -3 \color{red}{ -7x }\color{blue}{-5+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &15x & = &-8\\\Leftrightarrow & \color{red}{15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-8}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+5}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-x } & = & -7 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -7 \color{blue}{-5} \\\Leftrightarrow &-15x & = &-12\\\Leftrightarrow & \color{red}{-15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+9}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9-x } & = & 13 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 13 \color{blue}{-9} \\\Leftrightarrow &-10x & = &4\\\Leftrightarrow & \color{red}{-10}x & = &4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)