Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x } & = & -3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -3 \color{blue}{+6} \\\Leftrightarrow &-4x & = &3\\\Leftrightarrow & \color{red}{-4}x & = &3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{-8}& = & 15 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8+2x } & = & 15 \color{red}{ -2x }\color{blue}{+8+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & 15 \color{blue}{+8} \\\Leftrightarrow &11x & = &23\\\Leftrightarrow & \color{red}{11}x & = &23\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{23}{11} \\\Leftrightarrow & \color{green}{ x = \frac{23}{11} } & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+11}& = & -13 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11+13x } & = & -13 \color{red}{ -13x }\color{blue}{-11+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -13 \color{blue}{-11} \\\Leftrightarrow &20x & = &-24\\\Leftrightarrow & \color{red}{20}x & = &-24\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-24}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{-14}& = & -4 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14-4x } & = & -4 \color{red}{ +4x }\color{blue}{+14-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -4 \color{blue}{+14} \\\Leftrightarrow &-7x & = &10\\\Leftrightarrow & \color{red}{-7}x & = &10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-3}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3-x } & = & 12 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 12 \color{blue}{+3} \\\Leftrightarrow &-6x & = &15\\\Leftrightarrow & \color{red}{-6}x & = &15\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{15}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-x } & = & 4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-10\\\Leftrightarrow & \color{red}{-9}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{10}{9} } & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-13}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-7x } & = & 12 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 12 \color{blue}{+13} \\\Leftrightarrow &-13x & = &25\\\Leftrightarrow & \color{red}{-13}x & = &25\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{25}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{13} } & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-13}& = & -10 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13+13x } & = & -10 \color{red}{ -13x }\color{blue}{+13+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -10 \color{blue}{+13} \\\Leftrightarrow &24x & = &3\\\Leftrightarrow & \color{red}{24}x & = &3\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{3}{24} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{-6}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & 3x \color{red}{-6}\color{blue}{+6-11x } & = & 10 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & 3x \color{blue}{-11x } & = & 10 \color{blue}{+6} \\\Leftrightarrow &-8x & = &16\\\Leftrightarrow & \color{red}{-8}x & = &16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{16}{-8} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+1}& = & 13 \color{red}{ +3x } \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1-3x } & = & 13 \color{red}{ +3x }\color{blue}{-1-3x } \\\Leftrightarrow & -x \color{blue}{-3x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &-4x & = &12\\\Leftrightarrow & \color{red}{-4}x & = &12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{12}{-4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+8}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8-x } & = & -1 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -1 \color{blue}{-8} \\\Leftrightarrow &9x & = &-9\\\Leftrightarrow & \color{red}{9}x & = &-9\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-9}{9} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-10}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10-x } & = & -1 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -1 \color{blue}{+10} \\\Leftrightarrow &-12x & = &9\\\Leftrightarrow & \color{red}{-12}x & = &9\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{9}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)