Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-5}& = & 15 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{-5}\color{blue}{+5-3x } & = & 15 \color{red}{ +3x }\color{blue}{+5-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & 15 \color{blue}{+5} \\\Leftrightarrow &-14x & = &20\\\Leftrightarrow & \color{red}{-14}x & = &20\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{20}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{-9}& = & 13 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9+3x } & = & 13 \color{red}{ -3x }\color{blue}{+9+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 13 \color{blue}{+9} \\\Leftrightarrow &13x & = &22\\\Leftrightarrow & \color{red}{13}x & = &22\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{22}{13} \\\Leftrightarrow & \color{green}{ x = \frac{22}{13} } & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{-3}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-3}\color{blue}{+3-x } & = & -14 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -14 \color{blue}{+3} \\\Leftrightarrow &-15x & = &-11\\\Leftrightarrow & \color{red}{-15}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{11}{15} } & & \\ & V = \left\{ \frac{11}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+13}& = & -7 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13+5x } & = & -7 \color{red}{ -5x }\color{blue}{-13+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -7 \color{blue}{-13} \\\Leftrightarrow &8x & = &-20\\\Leftrightarrow & \color{red}{8}x & = &-20\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-20}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-7}& = & -8 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7+2x } & = & -8 \color{red}{ -2x }\color{blue}{+7+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & -8 \color{blue}{+7} \\\Leftrightarrow &13x & = &-1\\\Leftrightarrow & \color{red}{13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-2}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-2}\color{blue}{+2-x } & = & 7 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 7 \color{blue}{+2} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+14}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14-11x } & = & -1 \color{red}{ +11x }\color{blue}{-14-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &-16x & = &-15\\\Leftrightarrow & \color{red}{-16}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-15}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{15}{16} } & & \\ & V = \left\{ \frac{15}{16} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+5}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5-7x } & = & -7 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -7 \color{blue}{-5} \\\Leftrightarrow &-17x & = &-12\\\Leftrightarrow & \color{red}{-17}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-12}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{+13}& = & -6 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13-10x } & = & -6 \color{red}{ +10x }\color{blue}{-13-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & -6 \color{blue}{-13} \\\Leftrightarrow &-7x & = &-19\\\Leftrightarrow & \color{red}{-7}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{19}{7} } & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-4}& = & 4 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-4}\color{blue}{+4-4x } & = & 4 \color{red}{ +4x }\color{blue}{+4-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 4 \color{blue}{+4} \\\Leftrightarrow &-11x & = &8\\\Leftrightarrow & \color{red}{-11}x & = &8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+6}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+6}\color{blue}{-6-x } & = & 1 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 1 \color{blue}{-6} \\\Leftrightarrow &-7x & = &-5\\\Leftrightarrow & \color{red}{-7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-11}& = & -4 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11-11x } & = & -4 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -4 \color{blue}{+11} \\\Leftrightarrow &-9x & = &7\\\Leftrightarrow & \color{red}{-9}x & = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)