Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-5}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-5}\color{blue}{+5-x } & = & 12 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &-4x & = &17\\\Leftrightarrow & \color{red}{-4}x & = &17\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{17}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{4} } & & \\ & V = \left\{ \frac{-17}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+13}& = & -11 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{+13}\color{blue}{-13-9x } & = & -11 \color{red}{ +9x }\color{blue}{-13-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -11 \color{blue}{-13} \\\Leftrightarrow &-5x & = &-24\\\Leftrightarrow & \color{red}{-5}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-24}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{24}{5} } & & \\ & V = \left\{ \frac{24}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+5}& = & 7 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5+3x } & = & 7 \color{red}{ -3x }\color{blue}{-5+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 7 \color{blue}{-5} \\\Leftrightarrow &13x & = &2\\\Leftrightarrow & \color{red}{13}x & = &2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-6}& = & 15 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6+6x } & = & 15 \color{red}{ -6x }\color{blue}{+6+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & 15 \color{blue}{+6} \\\Leftrightarrow &13x & = &21\\\Leftrightarrow & \color{red}{13}x & = &21\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{21}{13} \\\Leftrightarrow & \color{green}{ x = \frac{21}{13} } & & \\ & V = \left\{ \frac{21}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-11}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-11}\color{blue}{+11-x } & = & -15 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -15 \color{blue}{+11} \\\Leftrightarrow &-3x & = &-4\\\Leftrightarrow & \color{red}{-3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-13}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13-x } & = & 2 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 2 \color{blue}{+13} \\\Leftrightarrow &-9x & = &15\\\Leftrightarrow & \color{red}{-9}x & = &15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+14}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14-x } & = & -7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -7 \color{blue}{-14} \\\Leftrightarrow &-10x & = &-21\\\Leftrightarrow & \color{red}{-10}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-21}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{21}{10} } & & \\ & V = \left\{ \frac{21}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{-9}& = & 7 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9-4x } & = & 7 \color{red}{ +4x }\color{blue}{+9-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & 7 \color{blue}{+9} \\\Leftrightarrow &11x & = &16\\\Leftrightarrow & \color{red}{11}x & = &16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9-x } & = & -9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &12x & = &-18\\\Leftrightarrow & \color{red}{12}x & = &-18\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-18}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+2}& = & 14 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+2}\color{blue}{-2+14x } & = & 14 \color{red}{ -14x }\color{blue}{-2+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 14 \color{blue}{-2} \\\Leftrightarrow &29x & = &12\\\Leftrightarrow & \color{red}{29}x & = &12\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{12}{29} \\\Leftrightarrow & \color{green}{ x = \frac{12}{29} } & & \\ & V = \left\{ \frac{12}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{-10}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-10}\color{blue}{+10-x } & = & 4 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 4 \color{blue}{+10} \\\Leftrightarrow &-10x & = &14\\\Leftrightarrow & \color{red}{-10}x & = &14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-14}& = & 12 \color{red}{ +8x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14-8x } & = & 12 \color{red}{ +8x }\color{blue}{+14-8x } \\\Leftrightarrow & 11x \color{blue}{-8x } & = & 12 \color{blue}{+14} \\\Leftrightarrow &3x & = &26\\\Leftrightarrow & \color{red}{3}x & = &26\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{26}{3} \\\Leftrightarrow & \color{green}{ x = \frac{26}{3} } & & \\ & V = \left\{ \frac{26}{3} \right\} & \\\end{align}\)