Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-7}& = & 1 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7+3x } & = & 1 \color{red}{ -3x }\color{blue}{+7+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 1 \color{blue}{+7} \\\Leftrightarrow &13x & = &8\\\Leftrightarrow & \color{red}{13}x & = &8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+3}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3-5x } & = & -9 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -9 \color{blue}{-3} \\\Leftrightarrow &x & = &-12\\\Leftrightarrow & \color{red}{}x & = &-12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -12 \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+10}& = & -3 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{+10}\color{blue}{-10-3x } & = & -3 \color{red}{ +3x }\color{blue}{-10-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & -3 \color{blue}{-10} \\\Leftrightarrow &-17x & = &-13\\\Leftrightarrow & \color{red}{-17}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-13}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{13}{17} } & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{-4}& = & -3 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-3x } & = & -3 \color{red}{ +3x }\color{blue}{+4-3x } \\\Leftrightarrow & -8x \color{blue}{-3x } & = & -3 \color{blue}{+4} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-10}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-x } & = & 10 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 10 \color{blue}{+10} \\\Leftrightarrow &-8x & = &20\\\Leftrightarrow & \color{red}{-8}x & = &20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-10}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-x } & = & -9 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -9 \color{blue}{+10} \\\Leftrightarrow &-13x & = &1\\\Leftrightarrow & \color{red}{-13}x & = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-5}& = & -6 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5+11x } & = & -6 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & -6 \color{blue}{+5} \\\Leftrightarrow &20x & = &-1\\\Leftrightarrow & \color{red}{20}x & = &-1\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-1}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{20} } & & \\ & V = \left\{ \frac{-1}{20} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{+13}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-x } & = & -13 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -13 \color{blue}{-13} \\\Leftrightarrow &-7x & = &-26\\\Leftrightarrow & \color{red}{-7}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-26}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{26}{7} } & & \\ & V = \left\{ \frac{26}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-5}& = & -3 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5+2x } & = & -3 \color{red}{ -2x }\color{blue}{+5+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -3 \color{blue}{+5} \\\Leftrightarrow &17x & = &2\\\Leftrightarrow & \color{red}{17}x & = &2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+3}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3-x } & = & 11 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 11 \color{blue}{-3} \\\Leftrightarrow &-15x & = &8\\\Leftrightarrow & \color{red}{-15}x & = &8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-12}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12-x } & = & 12 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &-14x & = &24\\\Leftrightarrow & \color{red}{-14}x & = &24\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{24}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-15}& = & -1 \color{red}{ +9x } \\\Leftrightarrow & 13x \color{red}{-15}\color{blue}{+15-9x } & = & -1 \color{red}{ +9x }\color{blue}{+15-9x } \\\Leftrightarrow & 13x \color{blue}{-9x } & = & -1 \color{blue}{+15} \\\Leftrightarrow &4x & = &14\\\Leftrightarrow & \color{red}{4}x & = &14\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{14}{4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)