Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+11}\color{blue}{-11-x } & = & 13 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+13}& = & -15 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13+5x } & = & -15 \color{red}{ -5x }\color{blue}{-13+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -15 \color{blue}{-13} \\\Leftrightarrow &11x & = &-28\\\Leftrightarrow & \color{red}{11}x & = &-28\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-28}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{11} } & & \\ & V = \left\{ \frac{-28}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-13}& = & -3 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-13}\color{blue}{+13-9x } & = & -3 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -3 \color{blue}{+13} \\\Leftrightarrow &-5x & = &10\\\Leftrightarrow & \color{red}{-5}x & = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+14}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14-x } & = & 13 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 13 \color{blue}{-14} \\\Leftrightarrow &x & = &-1\\\Leftrightarrow & \color{red}{}x & = &-1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -1 \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-7}& = & -7 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{-7}\color{blue}{+7+2x } & = & -7 \color{red}{ -2x }\color{blue}{+7+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-6}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6-x } & = & -11 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & -11 \color{blue}{+6} \\\Leftrightarrow &6x & = &-5\\\Leftrightarrow & \color{red}{6}x & = &-5\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-5}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-14}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-14}\color{blue}{+14-x } & = & -8 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -8 \color{blue}{+14} \\\Leftrightarrow &-6x & = &6\\\Leftrightarrow & \color{red}{-6}x & = &6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{6}{-6} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+9}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9-x } & = & -1 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -1 \color{blue}{-9} \\\Leftrightarrow &-10x & = &-10\\\Leftrightarrow & \color{red}{-10}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-10}{-10} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-14}& = & -4 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14+6x } & = & -4 \color{red}{ -6x }\color{blue}{+14+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -4 \color{blue}{+14} \\\Leftrightarrow &19x & = &10\\\Leftrightarrow & \color{red}{19}x & = &10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{10}{19} } & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-9}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-9}\color{blue}{+9-x } & = & 4 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 4 \color{blue}{+9} \\\Leftrightarrow &-13x & = &13\\\Leftrightarrow & \color{red}{-13}x & = &13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{13}{-13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+4}& = & -10 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4-4x } & = & -10 \color{red}{ +4x }\color{blue}{-4-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -10 \color{blue}{-4} \\\Leftrightarrow &-19x & = &-14\\\Leftrightarrow & \color{red}{-19}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-14}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{14}{19} } & & \\ & V = \left\{ \frac{14}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+14}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14-x } & = & 5 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 5 \color{blue}{-14} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)