Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+14}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14-x } & = & 8 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 8 \color{blue}{-14} \\\Leftrightarrow &-4x & = &-6\\\Leftrightarrow & \color{red}{-4}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{-5}& = & 13 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5+9x } & = & 13 \color{red}{ -9x }\color{blue}{+5+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &14x & = &18\\\Leftrightarrow & \color{red}{14}x & = &18\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{18}{14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-13}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13-x } & = & -8 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &-5x & = &5\\\Leftrightarrow & \color{red}{-5}x & = &5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{5}{-5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+12}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12-x } & = & -10 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -10 \color{blue}{-12} \\\Leftrightarrow &-12x & = &-22\\\Leftrightarrow & \color{red}{-12}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-22}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{-4}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-4}\color{blue}{+4-x } & = & -15 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -15 \color{blue}{+4} \\\Leftrightarrow &-5x & = &-11\\\Leftrightarrow & \color{red}{-5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+12}& = & 9 \color{red}{ +4x } \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12-4x } & = & 9 \color{red}{ +4x }\color{blue}{-12-4x } \\\Leftrightarrow & 5x \color{blue}{-4x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+9}& = & -7 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+9}\color{blue}{-9-6x } & = & -7 \color{red}{ +6x }\color{blue}{-9-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -7 \color{blue}{-9} \\\Leftrightarrow &-11x & = &-16\\\Leftrightarrow & \color{red}{-11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+4}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4-x } & = & -15 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -15 \color{blue}{-4} \\\Leftrightarrow &x & = &-19\\\Leftrightarrow & \color{red}{}x & = &-19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -19 \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+6}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+6}\color{blue}{-6-x } & = & -9 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -9 \color{blue}{-6} \\\Leftrightarrow &-14x & = &-15\\\Leftrightarrow & \color{red}{-14}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-15}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{15}{14} } & & \\ & V = \left\{ \frac{15}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{-5}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-x } & = & -14 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -14 \color{blue}{+5} \\\Leftrightarrow &-10x & = &-9\\\Leftrightarrow & \color{red}{-10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{-4}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4-x } & = & -5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &7x & = &-1\\\Leftrightarrow & \color{red}{7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+8}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+8}\color{blue}{-8-5x } & = & 1 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & 1 \color{blue}{-8} \\\Leftrightarrow &9x & = &-7\\\Leftrightarrow & \color{red}{9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-7}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)