Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(10x-14=-12-3x\)
2. \(14x+11=11+x\)
3. \(-4x-3=14+x\)
4. \(-2x-3=13+x\)
5. \(7x+9=-5-10x\)
6. \(-6x-8=-6+x\)
7. \(x+10=10+0x\)
8. \(-3x+3=11+x\)
9. \(-8x-13=-12+9x\)
10. \(10x+8=-15+9x\)
11. \(-2x+11=-2+5x\)
12. \(2x+7=-6+x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-14}& = & -12 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14+3x } & = & -12 \color{red}{ -3x }\color{blue}{+14+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -12 \color{blue}{+14} \\\Leftrightarrow &13x & = &2\\\Leftrightarrow & \color{red}{13}x & = &2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+11}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+11}\color{blue}{-11-x } & = & 11 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 11 \color{blue}{-11} \\\Leftrightarrow &13x & = &0\\\Leftrightarrow & \color{red}{13}x & = &0\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{0}{13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-3}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-3}\color{blue}{+3-x } & = & 14 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 14 \color{blue}{+3} \\\Leftrightarrow &-5x & = &17\\\Leftrightarrow & \color{red}{-5}x & = &17\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{17}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{5} } & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{-3}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-3}\color{blue}{+3-x } & = & 13 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 13 \color{blue}{+3} \\\Leftrightarrow &-3x & = &16\\\Leftrightarrow & \color{red}{-3}x & = &16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+9}& = & -5 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{+9}\color{blue}{-9+10x } & = & -5 \color{red}{ -10x }\color{blue}{-9+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & -5 \color{blue}{-9} \\\Leftrightarrow &17x & = &-14\\\Leftrightarrow & \color{red}{17}x & = &-14\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-14}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{17} } & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{-8}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-8}\color{blue}{+8-x } & = & -6 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -6 \color{blue}{+8} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+10}& = & 10 \color{red}{ +0x } \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10+0x } & = & 10 \color{red}{ +0x }\color{blue}{-10+0x } \\\Leftrightarrow & x \color{blue}{+0x } & = & 10 \color{blue}{-10} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+3}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-x } & = & 11 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 11 \color{blue}{-3} \\\Leftrightarrow &-4x & = &8\\\Leftrightarrow & \color{red}{-4}x & = &8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{8}{-4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-13}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13-9x } & = & -12 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -12 \color{blue}{+13} \\\Leftrightarrow &-17x & = &1\\\Leftrightarrow & \color{red}{-17}x & = &1\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{1}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{17} } & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+8}& = & -15 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8-9x } & = & -15 \color{red}{ +9x }\color{blue}{-8-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & -15 \color{blue}{-8} \\\Leftrightarrow &x & = &-23\\\Leftrightarrow & \color{red}{}x & = &-23\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -23 \\\Leftrightarrow & \color{green}{ x = -23 } & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+11}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-5x } & = & -2 \color{red}{ +5x }\color{blue}{-11-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & -2 \color{blue}{-11} \\\Leftrightarrow &-7x & = &-13\\\Leftrightarrow & \color{red}{-7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-13}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+7}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-x } & = & -6 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -6 \color{blue}{-7} \\\Leftrightarrow &x & = &-13\\\Leftrightarrow & \color{red}{}x & = &-13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -13 \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)