Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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