Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{+2}& = & -1 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+2}\color{blue}{-2-3x } & = & -1 \color{red}{ +3x }\color{blue}{-2-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & -1 \color{blue}{-2} \\\Leftrightarrow &-8x & = &-3\\\Leftrightarrow & \color{red}{-8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-9}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9-13x } & = & 8 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 8 \color{blue}{+9} \\\Leftrightarrow &-19x & = &17\\\Leftrightarrow & \color{red}{-19}x & = &17\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{17}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{19} } & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-1}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-1}\color{blue}{+1-x } & = & -15 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -15 \color{blue}{+1} \\\Leftrightarrow &-3x & = &-14\\\Leftrightarrow & \color{red}{-3}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-14}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{14}{3} } & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-2}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2-x } & = & -14 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -14 \color{blue}{+2} \\\Leftrightarrow &13x & = &-12\\\Leftrightarrow & \color{red}{13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+8}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8-x } & = & 14 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 14 \color{blue}{-8} \\\Leftrightarrow &-15x & = &6\\\Leftrightarrow & \color{red}{-15}x & = &6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-1}& = & -9 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1+5x } & = & -9 \color{red}{ -5x }\color{blue}{+1+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -9 \color{blue}{+1} \\\Leftrightarrow &11x & = &-8\\\Leftrightarrow & \color{red}{11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-8}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+15}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15-x } & = & -11 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -11 \color{blue}{-15} \\\Leftrightarrow &-6x & = &-26\\\Leftrightarrow & \color{red}{-6}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-26}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+13}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & 5x \color{red}{+13}\color{blue}{-13-13x } & = & -2 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & 5x \color{blue}{-13x } & = & -2 \color{blue}{-13} \\\Leftrightarrow &-8x & = &-15\\\Leftrightarrow & \color{red}{-8}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-15}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{15}{8} } & & \\ & V = \left\{ \frac{15}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-6}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6-11x } & = & 9 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 9 \color{blue}{+6} \\\Leftrightarrow &x & = &15\\\Leftrightarrow & \color{red}{}x & = &15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 15 \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-15}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15-x } & = & -14 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -14 \color{blue}{+15} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+8}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+8}\color{blue}{-8-9x } & = & -10 \color{red}{ +9x }\color{blue}{-8-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -10 \color{blue}{-8} \\\Leftrightarrow &-17x & = &-18\\\Leftrightarrow & \color{red}{-17}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-18}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{18}{17} } & & \\ & V = \left\{ \frac{18}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+13}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-x } & = & -9 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -9 \color{blue}{-13} \\\Leftrightarrow &-6x & = &-22\\\Leftrightarrow & \color{red}{-6}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-22}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)