Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+5}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5-x } & = & -1 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -1 \color{blue}{-5} \\\Leftrightarrow &-11x & = &-6\\\Leftrightarrow & \color{red}{-11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-12}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-12}\color{blue}{+12-x } & = & 3 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 3 \color{blue}{+12} \\\Leftrightarrow &-11x & = &15\\\Leftrightarrow & \color{red}{-11}x & = &15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{11} } & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+5}& = & -8 \color{red}{ +9x } \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5-9x } & = & -8 \color{red}{ +9x }\color{blue}{-5-9x } \\\Leftrightarrow & 13x \color{blue}{-9x } & = & -8 \color{blue}{-5} \\\Leftrightarrow &4x & = &-13\\\Leftrightarrow & \color{red}{4}x & = &-13\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-13}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{4} } & & \\ & V = \left\{ \frac{-13}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-6}& = & 10 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-6}\color{blue}{+6+14x } & = & 10 \color{red}{ -14x }\color{blue}{+6+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & 10 \color{blue}{+6} \\\Leftrightarrow &17x & = &16\\\Leftrightarrow & \color{red}{17}x & = &16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{16}{17} } & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-3}& = & -15 \color{red}{ +6x } \\\Leftrightarrow & -x \color{red}{-3}\color{blue}{+3-6x } & = & -15 \color{red}{ +6x }\color{blue}{+3-6x } \\\Leftrightarrow & -x \color{blue}{-6x } & = & -15 \color{blue}{+3} \\\Leftrightarrow &-7x & = &-12\\\Leftrightarrow & \color{red}{-7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{+4}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-11x } & = & 3 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 3 \color{blue}{-4} \\\Leftrightarrow &-18x & = &-1\\\Leftrightarrow & \color{red}{-18}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-1}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{18} } & & \\ & V = \left\{ \frac{1}{18} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+8}& = & 10 \color{red}{ -14x } \\\Leftrightarrow & x \color{red}{+8}\color{blue}{-8+14x } & = & 10 \color{red}{ -14x }\color{blue}{-8+14x } \\\Leftrightarrow & x \color{blue}{+14x } & = & 10 \color{blue}{-8} \\\Leftrightarrow &15x & = &2\\\Leftrightarrow & \color{red}{15}x & = &2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-2}& = & -8 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2-4x } & = & -8 \color{red}{ +4x }\color{blue}{+2-4x } \\\Leftrightarrow & 11x \color{blue}{-4x } & = & -8 \color{blue}{+2} \\\Leftrightarrow &7x & = &-6\\\Leftrightarrow & \color{red}{7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{+5}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-x } & = & -12 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -12 \color{blue}{-5} \\\Leftrightarrow &-15x & = &-17\\\Leftrightarrow & \color{red}{-15}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{17}{15} } & & \\ & V = \left\{ \frac{17}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+13}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13-x } & = & -15 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & -15 \color{blue}{-13} \\\Leftrightarrow &10x & = &-28\\\Leftrightarrow & \color{red}{10}x & = &-28\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-28}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{5} } & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+11}& = & -15 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11+4x } & = & -15 \color{red}{ -4x }\color{blue}{-11+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -15 \color{blue}{-11} \\\Leftrightarrow &9x & = &-26\\\Leftrightarrow & \color{red}{9}x & = &-26\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-26}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{9} } & & \\ & V = \left\{ \frac{-26}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+11}& = & 7 \color{red}{ -5x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11+5x } & = & 7 \color{red}{ -5x }\color{blue}{-11+5x } \\\Leftrightarrow & 13x \color{blue}{+5x } & = & 7 \color{blue}{-11} \\\Leftrightarrow &18x & = &-4\\\Leftrightarrow & \color{red}{18}x & = &-4\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{-4}{18} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)