Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+3}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3-11x } & = & -8 \color{red}{ +11x }\color{blue}{-3-11x } \\\Leftrightarrow & x \color{blue}{-11x } & = & -8 \color{blue}{-3} \\\Leftrightarrow &-10x & = &-11\\\Leftrightarrow & \color{red}{-10}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-11}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{10} } & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-10}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-10}\color{blue}{+10-x } & = & 3 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 3 \color{blue}{+10} \\\Leftrightarrow &5x & = &13\\\Leftrightarrow & \color{red}{5}x & = &13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-4}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-4}\color{blue}{+4-13x } & = & 9 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 9 \color{blue}{+4} \\\Leftrightarrow &-19x & = &13\\\Leftrightarrow & \color{red}{-19}x & = &13\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{13}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{19} } & & \\ & V = \left\{ \frac{-13}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{-13}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-13}\color{blue}{+13+11x } & = & 2 \color{red}{ -11x }\color{blue}{+13+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 2 \color{blue}{+13} \\\Leftrightarrow &15x & = &15\\\Leftrightarrow & \color{red}{15}x & = &15\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{15}{15} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-6}& = & -8 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6+7x } & = & -8 \color{red}{ -7x }\color{blue}{+6+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -8 \color{blue}{+6} \\\Leftrightarrow &15x & = &-2\\\Leftrightarrow & \color{red}{15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+15}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-x } & = & -7 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -7 \color{blue}{-15} \\\Leftrightarrow &x & = &-22\\\Leftrightarrow & \color{red}{}x & = &-22\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -22 \\\Leftrightarrow & \color{green}{ x = -22 } & & \\ & V = \left\{ -22 \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{-13}& = & -15 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13-8x } & = & -15 \color{red}{ +8x }\color{blue}{+13-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -15 \color{blue}{+13} \\\Leftrightarrow &-15x & = &-2\\\Leftrightarrow & \color{red}{-15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-1}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & 13x \color{red}{-1}\color{blue}{+1-7x } & = & -13 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & 13x \color{blue}{-7x } & = & -13 \color{blue}{+1} \\\Leftrightarrow &6x & = &-12\\\Leftrightarrow & \color{red}{6}x & = &-12\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-12}{6} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{-11}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11-x } & = & 9 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 9 \color{blue}{+11} \\\Leftrightarrow &-4x & = &20\\\Leftrightarrow & \color{red}{-4}x & = &20\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{20}{-4} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+14}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14-7x } & = & -13 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -13 \color{blue}{-14} \\\Leftrightarrow &3x & = &-27\\\Leftrightarrow & \color{red}{3}x & = &-27\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-27}{3} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+11}& = & -12 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11+7x } & = & -12 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -12 \color{blue}{-11} \\\Leftrightarrow &19x & = &-23\\\Leftrightarrow & \color{red}{19}x & = &-23\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-23}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{19} } & & \\ & V = \left\{ \frac{-23}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+14}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-x } & = & 12 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 12 \color{blue}{-14} \\\Leftrightarrow &-8x & = &-2\\\Leftrightarrow & \color{red}{-8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)