Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+10}& = & -6 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10-4x } & = & -6 \color{red}{ +4x }\color{blue}{-10-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & -6 \color{blue}{-10} \\\Leftrightarrow &5x & = &-16\\\Leftrightarrow & \color{red}{5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-16}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-12}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12-x } & = & 6 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 6 \color{blue}{+12} \\\Leftrightarrow &-10x & = &18\\\Leftrightarrow & \color{red}{-10}x & = &18\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{18}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+6}& = & 6 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{+6}\color{blue}{-6+5x } & = & 6 \color{red}{ -5x }\color{blue}{-6+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & 6 \color{blue}{-6} \\\Leftrightarrow &16x & = &0\\\Leftrightarrow & \color{red}{16}x & = &0\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{0}{16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{+10}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-x } & = & 12 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 12 \color{blue}{-10} \\\Leftrightarrow &-16x & = &2\\\Leftrightarrow & \color{red}{-16}x & = &2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+10}& = & 7 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{+10}\color{blue}{-10-3x } & = & 7 \color{red}{ +3x }\color{blue}{-10-3x } \\\Leftrightarrow & -8x \color{blue}{-3x } & = & 7 \color{blue}{-10} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-3}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3-x } & = & -4 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -4 \color{blue}{+3} \\\Leftrightarrow &-12x & = &-1\\\Leftrightarrow & \color{red}{-12}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-7}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7-7x } & = & 13 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & 13 \color{blue}{+7} \\\Leftrightarrow &-10x & = &20\\\Leftrightarrow & \color{red}{-10}x & = &20\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{20}{-10} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-14}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-14}\color{blue}{+14-13x } & = & 10 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 10 \color{blue}{+14} \\\Leftrightarrow &-28x & = &24\\\Leftrightarrow & \color{red}{-28}x & = &24\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{24}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+15}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+15}\color{blue}{-15-5x } & = & 3 \color{red}{ +5x }\color{blue}{-15-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 3 \color{blue}{-15} \\\Leftrightarrow &7x & = &-12\\\Leftrightarrow & \color{red}{7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-12}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{+15}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15-9x } & = & -13 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -13 \color{blue}{-15} \\\Leftrightarrow &-17x & = &-28\\\Leftrightarrow & \color{red}{-17}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-28}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{28}{17} } & & \\ & V = \left\{ \frac{28}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+2}& = & 15 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2+9x } & = & 15 \color{red}{ -9x }\color{blue}{-2+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &19x & = &13\\\Leftrightarrow & \color{red}{19}x & = &13\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{13}{19} \\\Leftrightarrow & \color{green}{ x = \frac{13}{19} } & & \\ & V = \left\{ \frac{13}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+13}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+13}\color{blue}{-13-x } & = & 10 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 10 \color{blue}{-13} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)