Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-2}& = & 12 \color{red}{ +8x } \\\Leftrightarrow & -x \color{red}{-2}\color{blue}{+2-8x } & = & 12 \color{red}{ +8x }\color{blue}{+2-8x } \\\Leftrightarrow & -x \color{blue}{-8x } & = & 12 \color{blue}{+2} \\\Leftrightarrow &-9x & = &14\\\Leftrightarrow & \color{red}{-9}x & = &14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{-14}& = & -7 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14+8x } & = & -7 \color{red}{ -8x }\color{blue}{+14+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -7 \color{blue}{+14} \\\Leftrightarrow &17x & = &7\\\Leftrightarrow & \color{red}{17}x & = &7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-2}& = & -12 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-2}\color{blue}{+2+11x } & = & -12 \color{red}{ -11x }\color{blue}{+2+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -12 \color{blue}{+2} \\\Leftrightarrow &14x & = &-10\\\Leftrightarrow & \color{red}{14}x & = &-10\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-10}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+13}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+13}\color{blue}{-13-x } & = & -3 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -3 \color{blue}{-13} \\\Leftrightarrow &-4x & = &-16\\\Leftrightarrow & \color{red}{-4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-16}{-4} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{-5}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-7x } & = & -13 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -13 \color{blue}{+5} \\\Leftrightarrow &-13x & = &-8\\\Leftrightarrow & \color{red}{-13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-11}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11-x } & = & 11 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 11 \color{blue}{+11} \\\Leftrightarrow &x & = &22\\\Leftrightarrow & \color{red}{}x & = &22\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 22 \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{+8}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8-x } & = & 11 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 11 \color{blue}{-8} \\\Leftrightarrow &5x & = &3\\\Leftrightarrow & \color{red}{5}x & = &3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+12}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+12}\color{blue}{-12-13x } & = & 15 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 15 \color{blue}{-12} \\\Leftrightarrow &-28x & = &3\\\Leftrightarrow & \color{red}{-28}x & = &3\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{3}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{28} } & & \\ & V = \left\{ \frac{-3}{28} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{+13}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-x } & = & 8 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 8 \color{blue}{-13} \\\Leftrightarrow &-6x & = &-5\\\Leftrightarrow & \color{red}{-6}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-10}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10-x } & = & 5 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 5 \color{blue}{+10} \\\Leftrightarrow &-14x & = &15\\\Leftrightarrow & \color{red}{-14}x & = &15\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{15}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{14} } & & \\ & V = \left\{ \frac{-15}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+4}\color{blue}{-4-x } & = & 5 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 5 \color{blue}{-4} \\\Leftrightarrow &-4x & = &1\\\Leftrightarrow & \color{red}{-4}x & = &1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{-1}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-1}\color{blue}{+1-x } & = & -11 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -11 \color{blue}{+1} \\\Leftrightarrow &-10x & = &-10\\\Leftrightarrow & \color{red}{-10}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-10}{-10} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)