Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-8}& = & -3 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-8}\color{blue}{+8+5x } & = & -3 \color{red}{ -5x }\color{blue}{+8+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -3 \color{blue}{+8} \\\Leftrightarrow &11x & = &5\\\Leftrightarrow & \color{red}{11}x & = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-5}& = & -11 \color{red}{ -12x } \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5+12x } & = & -11 \color{red}{ -12x }\color{blue}{+5+12x } \\\Leftrightarrow & -x \color{blue}{+12x } & = & -11 \color{blue}{+5} \\\Leftrightarrow &11x & = &-6\\\Leftrightarrow & \color{red}{11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-4}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4-x } & = & -10 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -10 \color{blue}{+4} \\\Leftrightarrow &-16x & = &-6\\\Leftrightarrow & \color{red}{-16}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+14}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+14}\color{blue}{-14-5x } & = & 10 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 10 \color{blue}{-14} \\\Leftrightarrow &7x & = &-4\\\Leftrightarrow & \color{red}{7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-14}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14-9x } & = & -10 \color{red}{ +9x }\color{blue}{+14-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -10 \color{blue}{+14} \\\Leftrightarrow &-17x & = &4\\\Leftrightarrow & \color{red}{-17}x & = &4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-7}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7-x } & = & -15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -15 \color{blue}{+7} \\\Leftrightarrow &-12x & = &-8\\\Leftrightarrow & \color{red}{-12}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+6}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6-x } & = & -10 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & -10 \color{blue}{-6} \\\Leftrightarrow &6x & = &-16\\\Leftrightarrow & \color{red}{6}x & = &-16\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-16}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+5}& = & 12 \color{red}{ +12x } \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5-12x } & = & 12 \color{red}{ +12x }\color{blue}{-5-12x } \\\Leftrightarrow & 7x \color{blue}{-12x } & = & 12 \color{blue}{-5} \\\Leftrightarrow &-5x & = &7\\\Leftrightarrow & \color{red}{-5}x & = &7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+6}& = & -15 \color{red}{ +12x } \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6-12x } & = & -15 \color{red}{ +12x }\color{blue}{-6-12x } \\\Leftrightarrow & 7x \color{blue}{-12x } & = & -15 \color{blue}{-6} \\\Leftrightarrow &-5x & = &-21\\\Leftrightarrow & \color{red}{-5}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-21}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{21}{5} } & & \\ & V = \left\{ \frac{21}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+13}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+13}\color{blue}{-13-x } & = & 11 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 11 \color{blue}{-13} \\\Leftrightarrow &-15x & = &-2\\\Leftrightarrow & \color{red}{-15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+13}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+13}\color{blue}{-13-x } & = & 12 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 12 \color{blue}{-13} \\\Leftrightarrow &4x & = &-1\\\Leftrightarrow & \color{red}{4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-1}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-2}& = & -3 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2-14x } & = & -3 \color{red}{ +14x }\color{blue}{+2-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & -3 \color{blue}{+2} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)