Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-6}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{-6}\color{blue}{+6-5x } & = & -15 \color{red}{ +5x }\color{blue}{+6-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & -15 \color{blue}{+6} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+14}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-x } & = & 14 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-1}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-1}\color{blue}{+1-x } & = & 15 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &-7x & = &16\\\Leftrightarrow & \color{red}{-7}x & = &16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{7} } & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+6}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+6}\color{blue}{-6-x } & = & -6 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -6 \color{blue}{-6} \\\Leftrightarrow &x & = &-12\\\Leftrightarrow & \color{red}{}x & = &-12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -12 \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+9}\color{blue}{-9-x } & = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+14}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14-x } & = & 3 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 3 \color{blue}{-14} \\\Leftrightarrow &9x & = &-11\\\Leftrightarrow & \color{red}{9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-11}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{9} } & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-12}& = & 9 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12+13x } & = & 9 \color{red}{ -13x }\color{blue}{+12+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 9 \color{blue}{+12} \\\Leftrightarrow &22x & = &21\\\Leftrightarrow & \color{red}{22}x & = &21\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{21}{22} \\\Leftrightarrow & \color{green}{ x = \frac{21}{22} } & & \\ & V = \left\{ \frac{21}{22} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+1}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1-4x } & = & -1 \color{red}{ +4x }\color{blue}{-1-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & -1 \color{blue}{-1} \\\Leftrightarrow &5x & = &-2\\\Leftrightarrow & \color{red}{5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-6}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-x } & = & 10 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 10 \color{blue}{+6} \\\Leftrightarrow &-15x & = &16\\\Leftrightarrow & \color{red}{-15}x & = &16\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{16}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{15} } & & \\ & V = \left\{ \frac{-16}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+7}& = & -7 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+7}\color{blue}{-7+13x } & = & -7 \color{red}{ -13x }\color{blue}{-7+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -7 \color{blue}{-7} \\\Leftrightarrow &20x & = &-14\\\Leftrightarrow & \color{red}{20}x & = &-14\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-14}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-7}& = & 5 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-7}\color{blue}{+7+3x } & = & 5 \color{red}{ -3x }\color{blue}{+7+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 5 \color{blue}{+7} \\\Leftrightarrow &10x & = &12\\\Leftrightarrow & \color{red}{10}x & = &12\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{12}{10} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-15}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-x } & = & 8 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 8 \color{blue}{+15} \\\Leftrightarrow &-5x & = &23\\\Leftrightarrow & \color{red}{-5}x & = &23\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{23}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{5} } & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)