Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{-15}& = & 1 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-15}\color{blue}{+15+12x } & = & 1 \color{red}{ -12x }\color{blue}{+15+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & 1 \color{blue}{+15} \\\Leftrightarrow &17x & = &16\\\Leftrightarrow & \color{red}{17}x & = &16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{16}{17} } & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-7}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7-7x } & = & -4 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & -4 \color{blue}{+7} \\\Leftrightarrow &5x & = &3\\\Leftrightarrow & \color{red}{5}x & = &3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12-x } & = & -8 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &11x & = &-20\\\Leftrightarrow & \color{red}{11}x & = &-20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-12}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12+11x } & = & 3 \color{red}{ -11x }\color{blue}{+12+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 3 \color{blue}{+12} \\\Leftrightarrow &23x & = &15\\\Leftrightarrow & \color{red}{23}x & = &15\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{15}{23} \\\Leftrightarrow & \color{green}{ x = \frac{15}{23} } & & \\ & V = \left\{ \frac{15}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+5}& = & -12 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5+6x } & = & -12 \color{red}{ -6x }\color{blue}{-5+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -12 \color{blue}{-5} \\\Leftrightarrow &19x & = &-17\\\Leftrightarrow & \color{red}{19}x & = &-17\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-17}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{19} } & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+1}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1-x } & = & -15 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -15 \color{blue}{-1} \\\Leftrightarrow &8x & = &-16\\\Leftrightarrow & \color{red}{8}x & = &-16\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-16}{8} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+6}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6-13x } & = & 6 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & 6 \color{blue}{-6} \\\Leftrightarrow &-10x & = &0\\\Leftrightarrow & \color{red}{-10}x & = &0\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{0}{-10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{-11}& = & -1 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11-14x } & = & -1 \color{red}{ +14x }\color{blue}{+11-14x } \\\Leftrightarrow & 15x \color{blue}{-14x } & = & -1 \color{blue}{+11} \\\Leftrightarrow &x & = &10\\\Leftrightarrow & \color{red}{}x & = &10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 10 \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-11}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-5x } & = & -8 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & -8 \color{blue}{+11} \\\Leftrightarrow &-19x & = &3\\\Leftrightarrow & \color{red}{-19}x & = &3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{19} } & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+12}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12+11x } & = & 11 \color{red}{ -11x }\color{blue}{-12+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &14x & = &-1\\\Leftrightarrow & \color{red}{14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-1}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{+9}& = & -6 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+9}\color{blue}{-9-5x } & = & -6 \color{red}{ +5x }\color{blue}{-9-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -6 \color{blue}{-9} \\\Leftrightarrow &-17x & = &-15\\\Leftrightarrow & \color{red}{-17}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-15}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{15}{17} } & & \\ & V = \left\{ \frac{15}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-1}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & 1 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 1 \color{blue}{+1} \\\Leftrightarrow &-15x & = &2\\\Leftrightarrow & \color{red}{-15}x & = &2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)