Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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