Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{-7}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-7}\color{blue}{+7-x } & = & -7 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{-14}& = & -7 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14-12x } & = & -7 \color{red}{ +12x }\color{blue}{+14-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & -7 \color{blue}{+14} \\\Leftrightarrow &-23x & = &7\\\Leftrightarrow & \color{red}{-23}x & = &7\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{7}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{23} } & & \\ & V = \left\{ \frac{-7}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{-10}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10-x } & = & 11 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 11 \color{blue}{+10} \\\Leftrightarrow &-15x & = &21\\\Leftrightarrow & \color{red}{-15}x & = &21\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{21}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{+10}& = & -2 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10+13x } & = & -2 \color{red}{ -13x }\color{blue}{-10+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -2 \color{blue}{-10} \\\Leftrightarrow &20x & = &-12\\\Leftrightarrow & \color{red}{20}x & = &-12\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-12}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+14}& = & 12 \color{red}{ +4x } \\\Leftrightarrow & 5x \color{red}{+14}\color{blue}{-14-4x } & = & 12 \color{red}{ +4x }\color{blue}{-14-4x } \\\Leftrightarrow & 5x \color{blue}{-4x } & = & 12 \color{blue}{-14} \\\Leftrightarrow &x & = &-2\\\Leftrightarrow & \color{red}{}x & = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+6}& = & 12 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6+7x } & = & 12 \color{red}{ -7x }\color{blue}{-6+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 12 \color{blue}{-6} \\\Leftrightarrow &19x & = &6\\\Leftrightarrow & \color{red}{19}x & = &6\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{6}{19} \\\Leftrightarrow & \color{green}{ x = \frac{6}{19} } & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+14}& = & -4 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14+3x } & = & -4 \color{red}{ -3x }\color{blue}{-14+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &13x & = &-18\\\Leftrightarrow & \color{red}{13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-18}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{13} } & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-14}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14-x } & = & -13 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -13 \color{blue}{+14} \\\Leftrightarrow &-14x & = &1\\\Leftrightarrow & \color{red}{-14}x & = &1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-7}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-x } & = & -15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -15 \color{blue}{+7} \\\Leftrightarrow &-11x & = &-8\\\Leftrightarrow & \color{red}{-11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+7}& = & 8 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7+11x } & = & 8 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 8 \color{blue}{-7} \\\Leftrightarrow &17x & = &1\\\Leftrightarrow & \color{red}{17}x & = &1\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{1}{17} \\\Leftrightarrow & \color{green}{ x = \frac{1}{17} } & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-8}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8-x } & = & 1 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+14}& = & 10 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+14}\color{blue}{-14-14x } & = & 10 \color{red}{ +14x }\color{blue}{-14-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 10 \color{blue}{-14} \\\Leftrightarrow &-25x & = &-4\\\Leftrightarrow & \color{red}{-25}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-4}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{4}{25} } & & \\ & V = \left\{ \frac{4}{25} \right\} & \\\end{align}\)