Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(-10x-9=-12+x\)
2. \(-x-12=-3+0x\)
3. \(12x+15=-9-7x\)
4. \(-15x-7=9+x\)
5. \(-3x+5=-3+x\)
6. \(12x+11=-11+5x\)
7. \(12x+8=-2-11x\)
8. \(7x-3=11+12x\)
9. \(-10x+3=12+x\)
10. \(-6x-6=15+13x\)
11. \(-6x-9=13+x\)
12. \(-13x+6=11+x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-9}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9-x } & = & -12 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -12 \color{blue}{+9} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-12}& = & -3 \color{red}{ +0x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12+0x } & = & -3 \color{red}{ +0x }\color{blue}{+12+0x } \\\Leftrightarrow & -x \color{blue}{+0x } & = & -3 \color{blue}{+12} \\\Leftrightarrow &-x & = &9\\\Leftrightarrow & \color{red}{-}x & = &9\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{9}{-1} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+15}& = & -9 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+15}\color{blue}{-15+7x } & = & -9 \color{red}{ -7x }\color{blue}{-15+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -9 \color{blue}{-15} \\\Leftrightarrow &19x & = &-24\\\Leftrightarrow & \color{red}{19}x & = &-24\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-24}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{19} } & & \\ & V = \left\{ \frac{-24}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-7}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7-x } & = & 9 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 9 \color{blue}{+7} \\\Leftrightarrow &-16x & = &16\\\Leftrightarrow & \color{red}{-16}x & = &16\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{16}{-16} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+5}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-x } & = & -3 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &-4x & = &-8\\\Leftrightarrow & \color{red}{-4}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-8}{-4} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+11}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11-5x } & = & -11 \color{red}{ +5x }\color{blue}{-11-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -11 \color{blue}{-11} \\\Leftrightarrow &7x & = &-22\\\Leftrightarrow & \color{red}{7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+8}& = & -2 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+8}\color{blue}{-8+11x } & = & -2 \color{red}{ -11x }\color{blue}{-8+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &23x & = &-10\\\Leftrightarrow & \color{red}{23}x & = &-10\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-10}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{23} } & & \\ & V = \left\{ \frac{-10}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-3}& = & 11 \color{red}{ +12x } \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3-12x } & = & 11 \color{red}{ +12x }\color{blue}{+3-12x } \\\Leftrightarrow & 7x \color{blue}{-12x } & = & 11 \color{blue}{+3} \\\Leftrightarrow &-5x & = &14\\\Leftrightarrow & \color{red}{-5}x & = &14\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{14}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{5} } & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+3}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3-x } & = & 12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 12 \color{blue}{-3} \\\Leftrightarrow &-11x & = &9\\\Leftrightarrow & \color{red}{-11}x & = &9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-6}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6-13x } & = & 15 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 15 \color{blue}{+6} \\\Leftrightarrow &-19x & = &21\\\Leftrightarrow & \color{red}{-19}x & = &21\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{21}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{19} } & & \\ & V = \left\{ \frac{-21}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-9}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9-x } & = & 13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 13 \color{blue}{+9} \\\Leftrightarrow &-7x & = &22\\\Leftrightarrow & \color{red}{-7}x & = &22\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{22}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+6}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+6}\color{blue}{-6-x } & = & 11 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 11 \color{blue}{-6} \\\Leftrightarrow &-14x & = &5\\\Leftrightarrow & \color{red}{-14}x & = &5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{14} } & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)