Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-7}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7-x } & = & 10 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 10 \color{blue}{+7} \\\Leftrightarrow &-13x & = &17\\\Leftrightarrow & \color{red}{-13}x & = &17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{-1}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1-x } & = & 6 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 6 \color{blue}{+1} \\\Leftrightarrow &-6x & = &7\\\Leftrightarrow & \color{red}{-6}x & = &7\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{7}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+8}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8-5x } & = & -11 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & -11 \color{blue}{-8} \\\Leftrightarrow &-7x & = &-19\\\Leftrightarrow & \color{red}{-7}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{19}{7} } & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-12}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12-7x } & = & 2 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &8x & = &14\\\Leftrightarrow & \color{red}{8}x & = &14\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{14}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+15}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15-x } & = & -15 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -15 \color{blue}{-15} \\\Leftrightarrow &-6x & = &-30\\\Leftrightarrow & \color{red}{-6}x & = &-30\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-30}{-6} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{+15}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+15}\color{blue}{-15-7x } & = & 13 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 13 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+9}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-x } & = & 2 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 2 \color{blue}{-9} \\\Leftrightarrow &-16x & = &-7\\\Leftrightarrow & \color{red}{-16}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-7}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{16} } & & \\ & V = \left\{ \frac{7}{16} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-12}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12-x } & = & -14 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -14 \color{blue}{+12} \\\Leftrightarrow &-9x & = &-2\\\Leftrightarrow & \color{red}{-9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+15}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15-x } & = & -8 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -8 \color{blue}{-15} \\\Leftrightarrow &-12x & = &-23\\\Leftrightarrow & \color{red}{-12}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-23}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{23}{12} } & & \\ & V = \left\{ \frac{23}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-3}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3-13x } & = & 10 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & 5x \color{blue}{-13x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &-8x & = &13\\\Leftrightarrow & \color{red}{-8}x & = &13\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{13}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{8} } & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-15}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15-x } & = & 9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 9 \color{blue}{+15} \\\Leftrightarrow &-11x & = &24\\\Leftrightarrow & \color{red}{-11}x & = &24\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{24}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{11} } & & \\ & V = \left\{ \frac{-24}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{-9}& = & -2 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-3x } & = & -2 \color{red}{ +3x }\color{blue}{+9-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -2 \color{blue}{+9} \\\Leftrightarrow &-5x & = &7\\\Leftrightarrow & \color{red}{-5}x & = &7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)