Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{+2}& = & 7 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+2}\color{blue}{-2+7x } & = & 7 \color{red}{ -7x }\color{blue}{-2+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 7 \color{blue}{-2} \\\Leftrightarrow &19x & = &5\\\Leftrightarrow & \color{red}{19}x & = &5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-12}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12-x } & = & 13 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 13 \color{blue}{+12} \\\Leftrightarrow &-14x & = &25\\\Leftrightarrow & \color{red}{-14}x & = &25\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{25}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{14} } & & \\ & V = \left\{ \frac{-25}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-12}& = & -6 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12+11x } & = & -6 \color{red}{ -11x }\color{blue}{+12+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -6 \color{blue}{+12} \\\Leftrightarrow &26x & = &6\\\Leftrightarrow & \color{red}{26}x & = &6\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{6}{26} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-6}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6-7x } & = & -14 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -14 \color{blue}{+6} \\\Leftrightarrow &-13x & = &-8\\\Leftrightarrow & \color{red}{-13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-1}& = & -6 \color{red}{ +14x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1-14x } & = & -6 \color{red}{ +14x }\color{blue}{+1-14x } \\\Leftrightarrow & -x \color{blue}{-14x } & = & -6 \color{blue}{+1} \\\Leftrightarrow &-15x & = &-5\\\Leftrightarrow & \color{red}{-15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+4}& = & -5 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4+7x } & = & -5 \color{red}{ -7x }\color{blue}{-4+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -5 \color{blue}{-4} \\\Leftrightarrow &15x & = &-9\\\Leftrightarrow & \color{red}{15}x & = &-9\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-9}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+13}& = & -1 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13+13x } & = & -1 \color{red}{ -13x }\color{blue}{-13+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & -1 \color{blue}{-13} \\\Leftrightarrow &21x & = &-14\\\Leftrightarrow & \color{red}{21}x & = &-14\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-14}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{+15}& = & -3 \color{red}{ +14x } \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15-14x } & = & -3 \color{red}{ +14x }\color{blue}{-15-14x } \\\Leftrightarrow & -x \color{blue}{-14x } & = & -3 \color{blue}{-15} \\\Leftrightarrow &-15x & = &-18\\\Leftrightarrow & \color{red}{-15}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-8}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8-13x } & = & -5 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & 7x \color{blue}{-13x } & = & -5 \color{blue}{+8} \\\Leftrightarrow &-6x & = &3\\\Leftrightarrow & \color{red}{-6}x & = &3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+1}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+1}\color{blue}{-1-5x } & = & 13 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &-3x & = &12\\\Leftrightarrow & \color{red}{-3}x & = &12\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{12}{-3} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+5}& = & -15 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+5}\color{blue}{-5+7x } & = & -15 \color{red}{ -7x }\color{blue}{-5+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &22x & = &-20\\\Leftrightarrow & \color{red}{22}x & = &-20\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-20}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+7}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7-x } & = & -9 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -9 \color{blue}{-7} \\\Leftrightarrow &-6x & = &-16\\\Leftrightarrow & \color{red}{-6}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-16}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)