Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+11}& = & 2 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11-10x } & = & 2 \color{red}{ +10x }\color{blue}{-11-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &-19x & = &-9\\\Leftrightarrow & \color{red}{-19}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-9}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{9}{19} } & & \\ & V = \left\{ \frac{9}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-3}& = & -6 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-3}\color{blue}{+3-9x } & = & -6 \color{red}{ +9x }\color{blue}{+3-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -6 \color{blue}{+3} \\\Leftrightarrow &-17x & = &-3\\\Leftrightarrow & \color{red}{-17}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+14}& = & -7 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+14}\color{blue}{-14+7x } & = & -7 \color{red}{ -7x }\color{blue}{-14+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -7 \color{blue}{-14} \\\Leftrightarrow &15x & = &-21\\\Leftrightarrow & \color{red}{15}x & = &-21\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-21}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-1}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1+11x } & = & -7 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -7 \color{blue}{+1} \\\Leftrightarrow &17x & = &-6\\\Leftrightarrow & \color{red}{17}x & = &-6\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-6}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{17} } & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{+11}& = & 10 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11+7x } & = & 10 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & 10 \color{blue}{-11} \\\Leftrightarrow &18x & = &-1\\\Leftrightarrow & \color{red}{18}x & = &-1\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{-1}{18} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{18} } & & \\ & V = \left\{ \frac{-1}{18} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-1}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1-7x } & = & 15 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &2x & = &16\\\Leftrightarrow & \color{red}{2}x & = &16\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{16}{2} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+1}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+1}\color{blue}{-1-x } & = & -10 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -10 \color{blue}{-1} \\\Leftrightarrow &-5x & = &-11\\\Leftrightarrow & \color{red}{-5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+2}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+2}\color{blue}{-2-x } & = & -6 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -6 \color{blue}{-2} \\\Leftrightarrow &12x & = &-8\\\Leftrightarrow & \color{red}{12}x & = &-8\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-8}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-12}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-x } & = & -11 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -11 \color{blue}{+12} \\\Leftrightarrow &-3x & = &1\\\Leftrightarrow & \color{red}{-3}x & = &1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-13}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-13}\color{blue}{+13-x } & = & 8 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 8 \color{blue}{+13} \\\Leftrightarrow &7x & = &21\\\Leftrightarrow & \color{red}{7}x & = &21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{21}{7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+3}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3-3x } & = & -11 \color{red}{ +3x }\color{blue}{-3-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & -11 \color{blue}{-3} \\\Leftrightarrow &-17x & = &-14\\\Leftrightarrow & \color{red}{-17}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-14}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{14}{17} } & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-5}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-x } & = & 5 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{+5} \\\Leftrightarrow &-6x & = &10\\\Leftrightarrow & \color{red}{-6}x & = &10\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{10}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)