Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{+5}& = & -8 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5+3x } & = & -8 \color{red}{ -3x }\color{blue}{-5+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -8 \color{blue}{-5} \\\Leftrightarrow &7x & = &-13\\\Leftrightarrow & \color{red}{7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-6}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6-x } & = & 6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 6 \color{blue}{+6} \\\Leftrightarrow &11x & = &12\\\Leftrightarrow & \color{red}{11}x & = &12\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{12}{11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{-7}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-x } & = & -6 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -6 \color{blue}{+7} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{+11}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11-x } & = & 4 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 4 \color{blue}{-11} \\\Leftrightarrow &-10x & = &-7\\\Leftrightarrow & \color{red}{-10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{-2}& = & -14 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2+6x } & = & -14 \color{red}{ -6x }\color{blue}{+2+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & -14 \color{blue}{+2} \\\Leftrightarrow &13x & = &-12\\\Leftrightarrow & \color{red}{13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{-13}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-13}\color{blue}{+13-x } & = & -4 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -4 \color{blue}{+13} \\\Leftrightarrow &-15x & = &9\\\Leftrightarrow & \color{red}{-15}x & = &9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-4}& = & 15 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4+12x } & = & 15 \color{red}{ -12x }\color{blue}{+4+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & 15 \color{blue}{+4} \\\Leftrightarrow &17x & = &19\\\Leftrightarrow & \color{red}{17}x & = &19\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{19}{17} \\\Leftrightarrow & \color{green}{ x = \frac{19}{17} } & & \\ & V = \left\{ \frac{19}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+11}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11-5x } & = & 13 \color{red}{ +5x }\color{blue}{-11-5x } \\\Leftrightarrow & 3x \color{blue}{-5x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &-2x & = &2\\\Leftrightarrow & \color{red}{-2}x & = &2\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{2}{-2} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+12}& = & 12 \color{red}{ +2x } \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12-2x } & = & 12 \color{red}{ +2x }\color{blue}{-12-2x } \\\Leftrightarrow & 13x \color{blue}{-2x } & = & 12 \color{blue}{-12} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+10}& = & -10 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+10}\color{blue}{-10+6x } & = & -10 \color{red}{ -6x }\color{blue}{-10+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -10 \color{blue}{-10} \\\Leftrightarrow &19x & = &-20\\\Leftrightarrow & \color{red}{19}x & = &-20\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-20}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{19} } & & \\ & V = \left\{ \frac{-20}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{+7}& = & -9 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+7}\color{blue}{-7-9x } & = & -9 \color{red}{ +9x }\color{blue}{-7-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -9 \color{blue}{-7} \\\Leftrightarrow &-13x & = &-16\\\Leftrightarrow & \color{red}{-13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-16}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{16}{13} } & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-14}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14-x } & = & 3 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 3 \color{blue}{+14} \\\Leftrightarrow &x & = &17\\\Leftrightarrow & \color{red}{}x & = &17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 17 \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)