Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-7}& = & 12 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-5x } & = & 12 \color{red}{ +5x }\color{blue}{+7-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & 12 \color{blue}{+7} \\\Leftrightarrow &-7x & = &19\\\Leftrightarrow & \color{red}{-7}x & = &19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{7} } & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+8}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-x } & = & 1 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 1 \color{blue}{-8} \\\Leftrightarrow &-11x & = &-7\\\Leftrightarrow & \color{red}{-11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+6}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6-13x } & = & -9 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -9 \color{blue}{-6} \\\Leftrightarrow &-3x & = &-15\\\Leftrightarrow & \color{red}{-3}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-15}{-3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+9}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9-x } & = & -5 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -5 \color{blue}{-9} \\\Leftrightarrow &-12x & = &-14\\\Leftrightarrow & \color{red}{-12}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-15}& = & 8 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-11x } & = & 8 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 8 \color{blue}{+15} \\\Leftrightarrow &-18x & = &23\\\Leftrightarrow & \color{red}{-18}x & = &23\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{23}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{18} } & & \\ & V = \left\{ \frac{-23}{18} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-7}& = & 3 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7-6x } & = & 3 \color{red}{ +6x }\color{blue}{+7-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & 3 \color{blue}{+7} \\\Leftrightarrow &-x & = &10\\\Leftrightarrow & \color{red}{-}x & = &10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{10}{-1} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+10}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-13x } & = & -1 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & -1 \color{blue}{-10} \\\Leftrightarrow &-18x & = &-11\\\Leftrightarrow & \color{red}{-18}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-11}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{11}{18} } & & \\ & V = \left\{ \frac{11}{18} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{+5}& = & 14 \color{red}{ +15x } \\\Leftrightarrow & -x \color{red}{+5}\color{blue}{-5-15x } & = & 14 \color{red}{ +15x }\color{blue}{-5-15x } \\\Leftrightarrow & -x \color{blue}{-15x } & = & 14 \color{blue}{-5} \\\Leftrightarrow &-16x & = &9\\\Leftrightarrow & \color{red}{-16}x & = &9\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{9}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{16} } & & \\ & V = \left\{ \frac{-9}{16} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+10}& = & -4 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+10}\color{blue}{-10+7x } & = & -4 \color{red}{ -7x }\color{blue}{-10+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -4 \color{blue}{-10} \\\Leftrightarrow &15x & = &-14\\\Leftrightarrow & \color{red}{15}x & = &-14\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-14}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{15} } & & \\ & V = \left\{ \frac{-14}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-1}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-x } & = & 9 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &-9x & = &10\\\Leftrightarrow & \color{red}{-9}x & = &10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{+11}& = & -14 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11+6x } & = & -14 \color{red}{ -6x }\color{blue}{-11+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &13x & = &-25\\\Leftrightarrow & \color{red}{13}x & = &-25\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-25}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{13} } & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-5}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-x } & = & 4 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 4 \color{blue}{+5} \\\Leftrightarrow &-6x & = &9\\\Leftrightarrow & \color{red}{-6}x & = &9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)