Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-8}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-8}\color{blue}{+8-x } & = & 6 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 6 \color{blue}{+8} \\\Leftrightarrow &7x & = &14\\\Leftrightarrow & \color{red}{7}x & = &14\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{14}{7} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-6}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x } & = & 3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 3 \color{blue}{+6} \\\Leftrightarrow &-4x & = &9\\\Leftrightarrow & \color{red}{-4}x & = &9\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{9}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+8}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+8}\color{blue}{-8-x } & = & 15 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 15 \color{blue}{-8} \\\Leftrightarrow &-13x & = &7\\\Leftrightarrow & \color{red}{-13}x & = &7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-13}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13-x } & = & 8 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 8 \color{blue}{+13} \\\Leftrightarrow &-14x & = &21\\\Leftrightarrow & \color{red}{-14}x & = &21\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{21}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-13}& = & -12 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13+7x } & = & -12 \color{red}{ -7x }\color{blue}{+13+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -12 \color{blue}{+13} \\\Leftrightarrow &19x & = &1\\\Leftrightarrow & \color{red}{19}x & = &1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+11}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+11}\color{blue}{-11-x } & = & 6 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 6 \color{blue}{-11} \\\Leftrightarrow &-4x & = &-5\\\Leftrightarrow & \color{red}{-4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+3}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-x } & = & 10 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 10 \color{blue}{-3} \\\Leftrightarrow &-4x & = &7\\\Leftrightarrow & \color{red}{-4}x & = &7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-14}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-14}\color{blue}{+14-x } & = & -5 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -5 \color{blue}{+14} \\\Leftrightarrow &-5x & = &9\\\Leftrightarrow & \color{red}{-5}x & = &9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-2}& = & -10 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2-11x } & = & -10 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -10 \color{blue}{+2} \\\Leftrightarrow &4x & = &-8\\\Leftrightarrow & \color{red}{4}x & = &-8\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-8}{4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+8}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+8}\color{blue}{-8+2x } & = & 2 \color{red}{ -2x }\color{blue}{-8+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 2 \color{blue}{-8} \\\Leftrightarrow &17x & = &-6\\\Leftrightarrow & \color{red}{17}x & = &-6\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-6}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{17} } & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+3}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3-x } & = & -2 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -2 \color{blue}{-3} \\\Leftrightarrow &-10x & = &-5\\\Leftrightarrow & \color{red}{-10}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-7}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7-x } & = & -15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -15 \color{blue}{+7} \\\Leftrightarrow &-13x & = &-8\\\Leftrightarrow & \color{red}{-13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)