Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+12}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12-x } & = & -9 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -9 \color{blue}{-12} \\\Leftrightarrow &x & = &-21\\\Leftrightarrow & \color{red}{}x & = &-21\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -21 \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-14}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14-x } & = & 6 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & 6 \color{blue}{+14} \\\Leftrightarrow &14x & = &20\\\Leftrightarrow & \color{red}{14}x & = &20\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{20}{14} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2-x } & = & -10 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &-12x & = &-12\\\Leftrightarrow & \color{red}{-12}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-12}{-12} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-x } & = & -10 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -10 \color{blue}{+2} \\\Leftrightarrow &-11x & = &-8\\\Leftrightarrow & \color{red}{-11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+3}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-7x } & = & -12 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -12 \color{blue}{-3} \\\Leftrightarrow &-13x & = &-15\\\Leftrightarrow & \color{red}{-13}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-15}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{15}{13} } & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-1}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-1}\color{blue}{+1-13x } & = & 2 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &-3x & = &3\\\Leftrightarrow & \color{red}{-3}x & = &3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{3}{-3} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{-15}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-x } & = & -14 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -14 \color{blue}{+15} \\\Leftrightarrow &-8x & = &1\\\Leftrightarrow & \color{red}{-8}x & = &1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+10}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{+10}\color{blue}{-10-7x } & = & 13 \color{red}{ +7x }\color{blue}{-10-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & 13 \color{blue}{-10} \\\Leftrightarrow &-3x & = &3\\\Leftrightarrow & \color{red}{-3}x & = &3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{3}{-3} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{+13}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13-13x } & = & -9 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & -9 \color{blue}{-13} \\\Leftrightarrow &-10x & = &-22\\\Leftrightarrow & \color{red}{-10}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-22}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+7}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7-7x } & = & -12 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &x & = &-19\\\Leftrightarrow & \color{red}{}x & = &-19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -19 \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{-2}& = & -13 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2+10x } & = & -13 \color{red}{ -10x }\color{blue}{+2+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & -13 \color{blue}{+2} \\\Leftrightarrow &21x & = &-11\\\Leftrightarrow & \color{red}{21}x & = &-11\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-11}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{21} } & & \\ & V = \left\{ \frac{-11}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+5}& = & -8 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5+13x } & = & -8 \color{red}{ -13x }\color{blue}{-5+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -8 \color{blue}{-5} \\\Leftrightarrow &23x & = &-13\\\Leftrightarrow & \color{red}{23}x & = &-13\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-13}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{23} } & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)