Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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