Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+5}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-x } & = & -2 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -2 \color{blue}{-5} \\\Leftrightarrow &-15x & = &-7\\\Leftrightarrow & \color{red}{-15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{+13}& = & -11 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13+8x } & = & -11 \color{red}{ -8x }\color{blue}{-13+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -11 \color{blue}{-13} \\\Leftrightarrow &11x & = &-24\\\Leftrightarrow & \color{red}{11}x & = &-24\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-24}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{11} } & & \\ & V = \left\{ \frac{-24}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{+14}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14-x } & = & -15 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -15 \color{blue}{-14} \\\Leftrightarrow &x & = &-29\\\Leftrightarrow & \color{red}{}x & = &-29\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -29 \\\Leftrightarrow & \color{green}{ x = -29 } & & \\ & V = \left\{ -29 \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+14}& = & 13 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14+2x } & = & 13 \color{red}{ -2x }\color{blue}{-14+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 13 \color{blue}{-14} \\\Leftrightarrow &13x & = &-1\\\Leftrightarrow & \color{red}{13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-10}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-10}\color{blue}{+10-11x } & = & -15 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -15 \color{blue}{+10} \\\Leftrightarrow &-5x & = &-5\\\Leftrightarrow & \color{red}{-5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-5}{-5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+4}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4-5x } & = & -4 \color{red}{ +5x }\color{blue}{-4-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & -4 \color{blue}{-4} \\\Leftrightarrow &-7x & = &-8\\\Leftrightarrow & \color{red}{-7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-8}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+14}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & -x \color{red}{+14}\color{blue}{-14-5x } & = & -4 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & -x \color{blue}{-5x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &-6x & = &-18\\\Leftrightarrow & \color{red}{-6}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-18}{-6} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+1}& = & -12 \color{red}{ +3x } \\\Leftrightarrow & x \color{red}{+1}\color{blue}{-1-3x } & = & -12 \color{red}{ +3x }\color{blue}{-1-3x } \\\Leftrightarrow & x \color{blue}{-3x } & = & -12 \color{blue}{-1} \\\Leftrightarrow &-2x & = &-13\\\Leftrightarrow & \color{red}{-2}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-13}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{13}{2} } & & \\ & V = \left\{ \frac{13}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-7}& = & 14 \color{red}{ +6x } \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7-6x } & = & 14 \color{red}{ +6x }\color{blue}{+7-6x } \\\Leftrightarrow & 13x \color{blue}{-6x } & = & 14 \color{blue}{+7} \\\Leftrightarrow &7x & = &21\\\Leftrightarrow & \color{red}{7}x & = &21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{21}{7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+4}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-x } & = & -8 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -8 \color{blue}{-4} \\\Leftrightarrow &-5x & = &-12\\\Leftrightarrow & \color{red}{-5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-6}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-6}\color{blue}{+6-x } & = & -7 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -7 \color{blue}{+6} \\\Leftrightarrow &-6x & = &-1\\\Leftrightarrow & \color{red}{-6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-7}& = & 9 \color{red}{ -2x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7+2x } & = & 9 \color{red}{ -2x }\color{blue}{+7+2x } \\\Leftrightarrow & -x \color{blue}{+2x } & = & 9 \color{blue}{+7} \\\Leftrightarrow &x & = &16\\\Leftrightarrow & \color{red}{}x & = &16\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 16 \\\Leftrightarrow & \color{green}{ x = 16 } & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)