Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+14}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-7x } & = & -6 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -6 \color{blue}{-14} \\\Leftrightarrow &-20x & = &-20\\\Leftrightarrow & \color{red}{-20}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-20}{-20} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+1}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1-7x } & = & 6 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &5x & = &5\\\Leftrightarrow & \color{red}{5}x & = &5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{5}{5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+8}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-x } & = & 14 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 14 \color{blue}{-8} \\\Leftrightarrow &-11x & = &6\\\Leftrightarrow & \color{red}{-11}x & = &6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+3}& = & 4 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+3}\color{blue}{-3+12x } & = & 4 \color{red}{ -12x }\color{blue}{-3+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & 4 \color{blue}{-3} \\\Leftrightarrow &25x & = &1\\\Leftrightarrow & \color{red}{25}x & = &1\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{1}{25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{25} } & & \\ & V = \left\{ \frac{1}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9-x } & = & -9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -9 \color{blue}{+9} \\\Leftrightarrow &-12x & = &0\\\Leftrightarrow & \color{red}{-12}x & = &0\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{0}{-12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+14}& = & 11 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{+14}\color{blue}{-14+13x } & = & 11 \color{red}{ -13x }\color{blue}{-14+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & 11 \color{blue}{-14} \\\Leftrightarrow &21x & = &-3\\\Leftrightarrow & \color{red}{21}x & = &-3\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-3}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+3}& = & -7 \color{red}{ +10x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-10x } & = & -7 \color{red}{ +10x }\color{blue}{-3-10x } \\\Leftrightarrow & -13x \color{blue}{-10x } & = & -7 \color{blue}{-3} \\\Leftrightarrow &-23x & = &-10\\\Leftrightarrow & \color{red}{-23}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-10}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{10}{23} } & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-15}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-15}\color{blue}{+15-x } & = & 7 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 7 \color{blue}{+15} \\\Leftrightarrow &-15x & = &22\\\Leftrightarrow & \color{red}{-15}x & = &22\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{22}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{15} } & & \\ & V = \left\{ \frac{-22}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-4}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4-7x } & = & -3 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -3 \color{blue}{+4} \\\Leftrightarrow &8x & = &1\\\Leftrightarrow & \color{red}{8}x & = &1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-3}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-3}\color{blue}{+3-x } & = & 15 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 15 \color{blue}{+3} \\\Leftrightarrow &-15x & = &18\\\Leftrightarrow & \color{red}{-15}x & = &18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+15}& = & -9 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15-9x } & = & -9 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & -9 \color{blue}{-15} \\\Leftrightarrow &x & = &-24\\\Leftrightarrow & \color{red}{}x & = &-24\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -24 \\\Leftrightarrow & \color{green}{ x = -24 } & & \\ & V = \left\{ -24 \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+1}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1-x } & = & -3 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -3 \color{blue}{-1} \\\Leftrightarrow &-10x & = &-4\\\Leftrightarrow & \color{red}{-10}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)