Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+9}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9-x } & = & 3 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 3 \color{blue}{-9} \\\Leftrightarrow &-10x & = &-6\\\Leftrightarrow & \color{red}{-10}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+6}& = & -3 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-10x } & = & -3 \color{red}{ +10x }\color{blue}{-6-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &-19x & = &-9\\\Leftrightarrow & \color{red}{-19}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-9}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{9}{19} } & & \\ & V = \left\{ \frac{9}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+8}& = & -5 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8-3x } & = & -5 \color{red}{ +3x }\color{blue}{-8-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & -5 \color{blue}{-8} \\\Leftrightarrow &7x & = &-13\\\Leftrightarrow & \color{red}{7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+14}& = & 8 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14+11x } & = & 8 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & 8 \color{blue}{-14} \\\Leftrightarrow &14x & = &-6\\\Leftrightarrow & \color{red}{14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+12}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+12}\color{blue}{-12-x } & = & -4 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -4 \color{blue}{-12} \\\Leftrightarrow &3x & = &-16\\\Leftrightarrow & \color{red}{3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-16}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-10}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-10}\color{blue}{+10-11x } & = & -11 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -11 \color{blue}{+10} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+4}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4-x } & = & -4 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -4 \color{blue}{-4} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-12}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-x } & = & -11 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -11 \color{blue}{+12} \\\Leftrightarrow &-16x & = &1\\\Leftrightarrow & \color{red}{-16}x & = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+13}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+13}\color{blue}{-13-13x } & = & -13 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -13 \color{blue}{-13} \\\Leftrightarrow &-28x & = &-26\\\Leftrightarrow & \color{red}{-28}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-26}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{13}{14} } & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{+5}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5-x } & = & -3 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &13x & = &-8\\\Leftrightarrow & \color{red}{13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+13}& = & 10 \color{red}{ +8x } \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13-8x } & = & 10 \color{red}{ +8x }\color{blue}{-13-8x } \\\Leftrightarrow & x \color{blue}{-8x } & = & 10 \color{blue}{-13} \\\Leftrightarrow &-7x & = &-3\\\Leftrightarrow & \color{red}{-7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-1}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-1}\color{blue}{+1-7x } & = & -1 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -1 \color{blue}{+1} \\\Leftrightarrow &-5x & = &0\\\Leftrightarrow & \color{red}{-5}x & = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)