Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{-8}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8-x } & = & 6 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 6 \color{blue}{+8} \\\Leftrightarrow &-9x & = &14\\\Leftrightarrow & \color{red}{-9}x & = &14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+12}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+12}\color{blue}{-12-x } & = & 14 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 14 \color{blue}{-12} \\\Leftrightarrow &-6x & = &2\\\Leftrightarrow & \color{red}{-6}x & = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{+8}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+8}\color{blue}{-8-x } & = & 15 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 15 \color{blue}{-8} \\\Leftrightarrow &-4x & = &7\\\Leftrightarrow & \color{red}{-4}x & = &7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{-9}& = & 9 \color{red}{ +12x } \\\Leftrightarrow & -7x \color{red}{-9}\color{blue}{+9-12x } & = & 9 \color{red}{ +12x }\color{blue}{+9-12x } \\\Leftrightarrow & -7x \color{blue}{-12x } & = & 9 \color{blue}{+9} \\\Leftrightarrow &-19x & = &18\\\Leftrightarrow & \color{red}{-19}x & = &18\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{18}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{19} } & & \\ & V = \left\{ \frac{-18}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-13}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-13}\color{blue}{+13-13x } & = & 10 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 10 \color{blue}{+13} \\\Leftrightarrow &-25x & = &23\\\Leftrightarrow & \color{red}{-25}x & = &23\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{23}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{25} } & & \\ & V = \left\{ \frac{-23}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-15}& = & 5 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15-3x } & = & 5 \color{red}{ +3x }\color{blue}{+15-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & 5 \color{blue}{+15} \\\Leftrightarrow &11x & = &20\\\Leftrightarrow & \color{red}{11}x & = &20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{20}{11} } & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+15}& = & -7 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15+4x } & = & -7 \color{red}{ -4x }\color{blue}{-15+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -7 \color{blue}{-15} \\\Leftrightarrow &13x & = &-22\\\Leftrightarrow & \color{red}{13}x & = &-22\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-22}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{13} } & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-7}\color{blue}{+7-x } & = & 14 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 14 \color{blue}{+7} \\\Leftrightarrow &-10x & = &21\\\Leftrightarrow & \color{red}{-10}x & = &21\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{21}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{10} } & & \\ & V = \left\{ \frac{-21}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-4}& = & 11 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-4}\color{blue}{+4-6x } & = & 11 \color{red}{ +6x }\color{blue}{+4-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &-17x & = &15\\\Leftrightarrow & \color{red}{-17}x & = &15\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{15}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{17} } & & \\ & V = \left\{ \frac{-15}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+15}& = & 8 \color{red}{ +2x } \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15-2x } & = & 8 \color{red}{ +2x }\color{blue}{-15-2x } \\\Leftrightarrow & 9x \color{blue}{-2x } & = & 8 \color{blue}{-15} \\\Leftrightarrow &7x & = &-7\\\Leftrightarrow & \color{red}{7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-7}{7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-2}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2-13x } & = & -6 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & -6 \color{blue}{+2} \\\Leftrightarrow &-7x & = &-4\\\Leftrightarrow & \color{red}{-7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+2}& = & 14 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2+2x } & = & 14 \color{red}{ -2x }\color{blue}{-2+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 14 \color{blue}{-2} \\\Leftrightarrow &13x & = &12\\\Leftrightarrow & \color{red}{13}x & = &12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)