Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+6}& = & 6 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6+9x } & = & 6 \color{red}{ -9x }\color{blue}{-6+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & 6 \color{blue}{-6} \\\Leftrightarrow &14x & = &0\\\Leftrightarrow & \color{red}{14}x & = &0\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{0}{14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+7}& = & 6 \color{red}{ +8x } \\\Leftrightarrow & 11x \color{red}{+7}\color{blue}{-7-8x } & = & 6 \color{red}{ +8x }\color{blue}{-7-8x } \\\Leftrightarrow & 11x \color{blue}{-8x } & = & 6 \color{blue}{-7} \\\Leftrightarrow &3x & = &-1\\\Leftrightarrow & \color{red}{3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-5}& = & 9 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5+3x } & = & 9 \color{red}{ -3x }\color{blue}{+5+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & 9 \color{blue}{+5} \\\Leftrightarrow &7x & = &14\\\Leftrightarrow & \color{red}{7}x & = &14\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{14}{7} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-9}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9-x } & = & -8 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &6x & = &1\\\Leftrightarrow & \color{red}{6}x & = &1\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{1}{6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-1}& = & -12 \color{red}{ +5x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1-5x } & = & -12 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & 9x \color{blue}{-5x } & = & -12 \color{blue}{+1} \\\Leftrightarrow &4x & = &-11\\\Leftrightarrow & \color{red}{4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-11}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+8}& = & 8 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+8}\color{blue}{-8-11x } & = & 8 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 8 \color{blue}{-8} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{-2}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-2}\color{blue}{+2-x } & = & 6 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 6 \color{blue}{+2} \\\Leftrightarrow &-15x & = &8\\\Leftrightarrow & \color{red}{-15}x & = &8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-4}& = & -8 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4+11x } & = & -8 \color{red}{ -11x }\color{blue}{+4+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -8 \color{blue}{+4} \\\Leftrightarrow &15x & = &-4\\\Leftrightarrow & \color{red}{15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-4}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-13}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13-11x } & = & 9 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & 9 \color{blue}{+13} \\\Leftrightarrow &-6x & = &22\\\Leftrightarrow & \color{red}{-6}x & = &22\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{22}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-4}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-4}\color{blue}{+4-x } & = & 6 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 6 \color{blue}{+4} \\\Leftrightarrow &-7x & = &10\\\Leftrightarrow & \color{red}{-7}x & = &10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-12}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12-13x } & = & -4 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -4 \color{blue}{+12} \\\Leftrightarrow &-25x & = &8\\\Leftrightarrow & \color{red}{-25}x & = &8\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{8}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{25} } & & \\ & V = \left\{ \frac{-8}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-1}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-1}\color{blue}{+1-x } & = & -9 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -9 \color{blue}{+1} \\\Leftrightarrow &7x & = &-8\\\Leftrightarrow & \color{red}{7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-8}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)