Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{-9}& = & -15 \color{red}{ -6x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9+6x } & = & -15 \color{red}{ -6x }\color{blue}{+9+6x } \\\Leftrightarrow & x \color{blue}{+6x } & = & -15 \color{blue}{+9} \\\Leftrightarrow &7x & = &-6\\\Leftrightarrow & \color{red}{7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+3}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -x \color{red}{+3}\color{blue}{-3-13x } & = & -7 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & -x \color{blue}{-13x } & = & -7 \color{blue}{-3} \\\Leftrightarrow &-14x & = &-10\\\Leftrightarrow & \color{red}{-14}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+6}& = & -15 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-6x } & = & -15 \color{red}{ +6x }\color{blue}{-6-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -15 \color{blue}{-6} \\\Leftrightarrow &-11x & = &-21\\\Leftrightarrow & \color{red}{-11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+15}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15-11x } & = & -9 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & -9 \color{blue}{-15} \\\Leftrightarrow &-7x & = &-24\\\Leftrightarrow & \color{red}{-7}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-24}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{24}{7} } & & \\ & V = \left\{ \frac{24}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{+10}& = & 2 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-14x } & = & 2 \color{red}{ +14x }\color{blue}{-10-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 2 \color{blue}{-10} \\\Leftrightarrow &-25x & = &-8\\\Leftrightarrow & \color{red}{-25}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-8}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{8}{25} } & & \\ & V = \left\{ \frac{8}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{+11}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & x \color{red}{+11}\color{blue}{-11+7x } & = & 2 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & x \color{blue}{+7x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &8x & = &-9\\\Leftrightarrow & \color{red}{8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-9}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9-x } & = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-8}& = & 1 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8-12x } & = & 1 \color{red}{ +12x }\color{blue}{+8-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &-23x & = &9\\\Leftrightarrow & \color{red}{-23}x & = &9\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{9}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{23} } & & \\ & V = \left\{ \frac{-9}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-4}& = & 15 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4+14x } & = & 15 \color{red}{ -14x }\color{blue}{+4+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 15 \color{blue}{+4} \\\Leftrightarrow &29x & = &19\\\Leftrightarrow & \color{red}{29}x & = &19\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{19}{29} \\\Leftrightarrow & \color{green}{ x = \frac{19}{29} } & & \\ & V = \left\{ \frac{19}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+3}& = & 11 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+3}\color{blue}{-3-11x } & = & 11 \color{red}{ +11x }\color{blue}{-3-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 11 \color{blue}{-3} \\\Leftrightarrow &-9x & = &8\\\Leftrightarrow & \color{red}{-9}x & = &8\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{8}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{-13}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13-x } & = & -14 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & -14 \color{blue}{+13} \\\Leftrightarrow &10x & = &-1\\\Leftrightarrow & \color{red}{10}x & = &-1\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-1}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{-2}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2-13x } & = & 9 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 9 \color{blue}{+2} \\\Leftrightarrow &-19x & = &11\\\Leftrightarrow & \color{red}{-19}x & = &11\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{11}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{19} } & & \\ & V = \left\{ \frac{-11}{19} \right\} & \\\end{align}\)