Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-4}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-4}\color{blue}{+4-x } & = & 15 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 15 \color{blue}{+4} \\\Leftrightarrow &-8x & = &19\\\Leftrightarrow & \color{red}{-8}x & = &19\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{19}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{8} } & & \\ & V = \left\{ \frac{-19}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+3}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+3}\color{blue}{-3-11x } & = & 5 \color{red}{ +11x }\color{blue}{-3-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 5 \color{blue}{-3} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-1}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-11x } & = & -8 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & -8x \color{blue}{-11x } & = & -8 \color{blue}{+1} \\\Leftrightarrow &-19x & = &-7\\\Leftrightarrow & \color{red}{-19}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-7}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+11}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11-7x } & = & 11 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 11 \color{blue}{-11} \\\Leftrightarrow &-17x & = &0\\\Leftrightarrow & \color{red}{-17}x & = &0\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{0}{-17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-12}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12-x } & = & 8 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & 8 \color{blue}{+12} \\\Leftrightarrow &10x & = &20\\\Leftrightarrow & \color{red}{10}x & = &20\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{20}{10} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+8}& = & -14 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+8}\color{blue}{-8+2x } & = & -14 \color{red}{ -2x }\color{blue}{-8+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -14 \color{blue}{-8} \\\Leftrightarrow &17x & = &-22\\\Leftrightarrow & \color{red}{17}x & = &-22\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-22}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{17} } & & \\ & V = \left\{ \frac{-22}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+13}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-x } & = & 14 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 14 \color{blue}{-13} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-2}\color{blue}{+2-x } & = & 15 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 15 \color{blue}{+2} \\\Leftrightarrow &-10x & = &17\\\Leftrightarrow & \color{red}{-10}x & = &17\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{17}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{10} } & & \\ & V = \left\{ \frac{-17}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-13}& = & -2 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-9x } & = & -2 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & -2 \color{blue}{+13} \\\Leftrightarrow &-20x & = &11\\\Leftrightarrow & \color{red}{-20}x & = &11\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{11}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{20} } & & \\ & V = \left\{ \frac{-11}{20} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{-5}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5-x } & = & -7 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -7 \color{blue}{+5} \\\Leftrightarrow &-3x & = &-2\\\Leftrightarrow & \color{red}{-3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-12}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-12}\color{blue}{+12-x } & = & -14 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -14 \color{blue}{+12} \\\Leftrightarrow &-15x & = &-2\\\Leftrightarrow & \color{red}{-15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-3}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3-x } & = & 9 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 9 \color{blue}{+3} \\\Leftrightarrow &-6x & = &12\\\Leftrightarrow & \color{red}{-6}x & = &12\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{12}{-6} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)