Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-7}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-x } & = & -6 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -6 \color{blue}{+7} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-11}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-11}\color{blue}{+11-9x } & = & 8 \color{red}{ +9x }\color{blue}{+11-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 8 \color{blue}{+11} \\\Leftrightarrow &5x & = &19\\\Leftrightarrow & \color{red}{5}x & = &19\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{19}{5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-13}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13-11x } & = & 14 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 14 \color{blue}{+13} \\\Leftrightarrow &x & = &27\\\Leftrightarrow & \color{red}{}x & = &27\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 27 \\\Leftrightarrow & \color{green}{ x = 27 } & & \\ & V = \left\{ 27 \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-2}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-2}\color{blue}{+2-7x } & = & 2 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 2 \color{blue}{+2} \\\Leftrightarrow &-20x & = &4\\\Leftrightarrow & \color{red}{-20}x & = &4\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{4}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{-13}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-x } & = & -7 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -7 \color{blue}{+13} \\\Leftrightarrow &-11x & = &6\\\Leftrightarrow & \color{red}{-11}x & = &6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-2}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-2}\color{blue}{+2-x } & = & 11 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 11 \color{blue}{+2} \\\Leftrightarrow &-3x & = &13\\\Leftrightarrow & \color{red}{-3}x & = &13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{-8}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8-x } & = & 1 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &-10x & = &9\\\Leftrightarrow & \color{red}{-10}x & = &9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-8}& = & 8 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8-11x } & = & 8 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 8 \color{blue}{+8} \\\Leftrightarrow &-18x & = &16\\\Leftrightarrow & \color{red}{-18}x & = &16\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{16}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+9}& = & -6 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9-9x } & = & -6 \color{red}{ +9x }\color{blue}{-9-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -6 \color{blue}{-9} \\\Leftrightarrow &-5x & = &-15\\\Leftrightarrow & \color{red}{-5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-15}{-5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+8}& = & -12 \color{red}{ +4x } \\\Leftrightarrow & -x \color{red}{+8}\color{blue}{-8-4x } & = & -12 \color{red}{ +4x }\color{blue}{-8-4x } \\\Leftrightarrow & -x \color{blue}{-4x } & = & -12 \color{blue}{-8} \\\Leftrightarrow &-5x & = &-20\\\Leftrightarrow & \color{red}{-5}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-20}{-5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+3}& = & 15 \color{red}{ +9x } \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3-9x } & = & 15 \color{red}{ +9x }\color{blue}{-3-9x } \\\Leftrightarrow & 5x \color{blue}{-9x } & = & 15 \color{blue}{-3} \\\Leftrightarrow &-4x & = &12\\\Leftrightarrow & \color{red}{-4}x & = &12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{12}{-4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+3}& = & -11 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3+3x } & = & -11 \color{red}{ -3x }\color{blue}{-3+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -11 \color{blue}{-3} \\\Leftrightarrow &7x & = &-14\\\Leftrightarrow & \color{red}{7}x & = &-14\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-14}{7} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)