Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+11}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11-7x } & = & -4 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -x \color{blue}{-7x } & = & -4 \color{blue}{-11} \\\Leftrightarrow &-8x & = &-15\\\Leftrightarrow & \color{red}{-8}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-15}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{15}{8} } & & \\ & V = \left\{ \frac{15}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-8}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-8}\color{blue}{+8-x } & = & 2 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 2 \color{blue}{+8} \\\Leftrightarrow &-3x & = &10\\\Leftrightarrow & \color{red}{-3}x & = &10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{-13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-x } & = & 4 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 4 \color{blue}{+13} \\\Leftrightarrow &-11x & = &17\\\Leftrightarrow & \color{red}{-11}x & = &17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-1}& = & -2 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1-9x } & = & -2 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -2 \color{blue}{+1} \\\Leftrightarrow &5x & = &-1\\\Leftrightarrow & \color{red}{5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-7}& = & 5 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7-4x } & = & 5 \color{red}{ +4x }\color{blue}{+7-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & 5 \color{blue}{+7} \\\Leftrightarrow &-7x & = &12\\\Leftrightarrow & \color{red}{-7}x & = &12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-1}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1-x } & = & -9 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -9 \color{blue}{+1} \\\Leftrightarrow &5x & = &-8\\\Leftrightarrow & \color{red}{5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{+2}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2-9x } & = & -14 \color{red}{ +9x }\color{blue}{-2-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -14 \color{blue}{-2} \\\Leftrightarrow &-5x & = &-16\\\Leftrightarrow & \color{red}{-5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-5}& = & -4 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5+5x } & = & -4 \color{red}{ -5x }\color{blue}{+5+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -4 \color{blue}{+5} \\\Leftrightarrow &11x & = &1\\\Leftrightarrow & \color{red}{11}x & = &1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+5}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+5}\color{blue}{-5-x } & = & -2 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & -2 \color{blue}{-5} \\\Leftrightarrow &10x & = &-7\\\Leftrightarrow & \color{red}{10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-7}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-14}& = & -6 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14-6x } & = & -6 \color{red}{ +6x }\color{blue}{+14-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & -6 \color{blue}{+14} \\\Leftrightarrow &-17x & = &8\\\Leftrightarrow & \color{red}{-17}x & = &8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{17} } & & \\ & V = \left\{ \frac{-8}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+14}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+14}\color{blue}{-14-x } & = & -12 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -12 \color{blue}{-14} \\\Leftrightarrow &-15x & = &-26\\\Leftrightarrow & \color{red}{-15}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-26}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{26}{15} } & & \\ & V = \left\{ \frac{26}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-11}& = & -4 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11-4x } & = & -4 \color{red}{ +4x }\color{blue}{+11-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -4 \color{blue}{+11} \\\Leftrightarrow &-7x & = &7\\\Leftrightarrow & \color{red}{-7}x & = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)