Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-6}& = & -14 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-6}\color{blue}{+6-5x } & = & -14 \color{red}{ +5x }\color{blue}{+6-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -14 \color{blue}{+6} \\\Leftrightarrow &x & = &-8\\\Leftrightarrow & \color{red}{}x & = &-8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -8 \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-9}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9-7x } & = & 9 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 9 \color{blue}{+9} \\\Leftrightarrow &-17x & = &18\\\Leftrightarrow & \color{red}{-17}x & = &18\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{18}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{17} } & & \\ & V = \left\{ \frac{-18}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+11}& = & 1 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11+11x } & = & 1 \color{red}{ -11x }\color{blue}{-11+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 1 \color{blue}{-11} \\\Leftrightarrow &23x & = &-10\\\Leftrightarrow & \color{red}{23}x & = &-10\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-10}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{23} } & & \\ & V = \left\{ \frac{-10}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+8}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8-13x } & = & -9 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & -9 \color{blue}{-8} \\\Leftrightarrow &-11x & = &-17\\\Leftrightarrow & \color{red}{-11}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-15}& = & 5 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15-7x } & = & 5 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & 5 \color{blue}{+15} \\\Leftrightarrow &x & = &20\\\Leftrightarrow & \color{red}{}x & = &20\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 20 \\\Leftrightarrow & \color{green}{ x = 20 } & & \\ & V = \left\{ 20 \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+14}& = & 9 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14+3x } & = & 9 \color{red}{ -3x }\color{blue}{-14+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 9 \color{blue}{-14} \\\Leftrightarrow &13x & = &-5\\\Leftrightarrow & \color{red}{13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+10}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-x } & = & 6 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 6 \color{blue}{-10} \\\Leftrightarrow &-16x & = &-4\\\Leftrightarrow & \color{red}{-16}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+12}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12-x } & = & 9 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &-15x & = &-3\\\Leftrightarrow & \color{red}{-15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+14}& = & 9 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14+3x } & = & 9 \color{red}{ -3x }\color{blue}{-14+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & 9 \color{blue}{-14} \\\Leftrightarrow &7x & = &-5\\\Leftrightarrow & \color{red}{7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-10}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-10}\color{blue}{+10+13x } & = & 14 \color{red}{ -13x }\color{blue}{+10+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 14 \color{blue}{+10} \\\Leftrightarrow &22x & = &24\\\Leftrightarrow & \color{red}{22}x & = &24\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{24}{22} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{+11}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+11}\color{blue}{-11-x } & = & -11 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -11 \color{blue}{-11} \\\Leftrightarrow &-13x & = &-22\\\Leftrightarrow & \color{red}{-13}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-22}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{22}{13} } & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+15}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15-x } & = & 2 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 2 \color{blue}{-15} \\\Leftrightarrow &-14x & = &-13\\\Leftrightarrow & \color{red}{-14}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-13}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{14} } & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)