Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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