Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+10}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+10}\color{blue}{-10-13x } & = & 3 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 3 \color{blue}{-10} \\\Leftrightarrow &-25x & = &-7\\\Leftrightarrow & \color{red}{-25}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-7}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{7}{25} } & & \\ & V = \left\{ \frac{7}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+5}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-13x } & = & -3 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &-16x & = &-8\\\Leftrightarrow & \color{red}{-16}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-8}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+4}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4-x } & = & -11 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -11 \color{blue}{-4} \\\Leftrightarrow &7x & = &-15\\\Leftrightarrow & \color{red}{7}x & = &-15\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-15}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-6}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-6}\color{blue}{+6-9x } & = & 12 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & 12 \color{blue}{+6} \\\Leftrightarrow &-20x & = &18\\\Leftrightarrow & \color{red}{-20}x & = &18\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{18}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+8}& = & -11 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+8}\color{blue}{-8+11x } & = & -11 \color{red}{ -11x }\color{blue}{-8+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -11 \color{blue}{-8} \\\Leftrightarrow &23x & = &-19\\\Leftrightarrow & \color{red}{23}x & = &-19\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-19}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{23} } & & \\ & V = \left\{ \frac{-19}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-15}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-x } & = & -9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -9 \color{blue}{+15} \\\Leftrightarrow &-12x & = &6\\\Leftrightarrow & \color{red}{-12}x & = &6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+10}& = & 1 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+10}\color{blue}{-10+8x } & = & 1 \color{red}{ -8x }\color{blue}{-10+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 1 \color{blue}{-10} \\\Leftrightarrow &11x & = &-9\\\Leftrightarrow & \color{red}{11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{-9}& = & -2 \color{red}{ -7x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9+7x } & = & -2 \color{red}{ -7x }\color{blue}{+9+7x } \\\Leftrightarrow & x \color{blue}{+7x } & = & -2 \color{blue}{+9} \\\Leftrightarrow &8x & = &7\\\Leftrightarrow & \color{red}{8}x & = &7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-1}& = & -13 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1-8x } & = & -13 \color{red}{ +8x }\color{blue}{+1-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & -13 \color{blue}{+1} \\\Leftrightarrow &-13x & = &-12\\\Leftrightarrow & \color{red}{-13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-14}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14-7x } & = & 6 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & 6 \color{blue}{+14} \\\Leftrightarrow &5x & = &20\\\Leftrightarrow & \color{red}{5}x & = &20\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{20}{5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+6}& = & -9 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6+11x } & = & -9 \color{red}{ -11x }\color{blue}{-6+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & -9 \color{blue}{-6} \\\Leftrightarrow &20x & = &-15\\\Leftrightarrow & \color{red}{20}x & = &-15\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-15}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+2}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-11x } & = & -3 \color{red}{ +11x }\color{blue}{-2-11x } \\\Leftrightarrow & -8x \color{blue}{-11x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &-19x & = &-5\\\Leftrightarrow & \color{red}{-19}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-5}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)