Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-8}& = & -3 \color{red}{ +8x } \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8-8x } & = & -3 \color{red}{ +8x }\color{blue}{+8-8x } \\\Leftrightarrow & 15x \color{blue}{-8x } & = & -3 \color{blue}{+8} \\\Leftrightarrow &7x & = &5\\\Leftrightarrow & \color{red}{7}x & = &5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-6}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-6}\color{blue}{+6-x } & = & 1 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 1 \color{blue}{+6} \\\Leftrightarrow &-9x & = &7\\\Leftrightarrow & \color{red}{-9}x & = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+2}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2-7x } & = & -11 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -11 \color{blue}{-2} \\\Leftrightarrow &-17x & = &-13\\\Leftrightarrow & \color{red}{-17}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-13}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{13}{17} } & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-5}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-x } & = & -13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -13 \color{blue}{+5} \\\Leftrightarrow &x & = &-8\\\Leftrightarrow & \color{red}{}x & = &-8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -8 \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-14}& = & 10 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14+13x } & = & 10 \color{red}{ -13x }\color{blue}{+14+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 10 \color{blue}{+14} \\\Leftrightarrow &24x & = &24\\\Leftrightarrow & \color{red}{24}x & = &24\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{24}{24} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+11}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11-13x } & = & 12 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & 5x \color{blue}{-13x } & = & 12 \color{blue}{-11} \\\Leftrightarrow &-8x & = &1\\\Leftrightarrow & \color{red}{-8}x & = &1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+3}& = & -4 \color{red}{ +4x } \\\Leftrightarrow & -x \color{red}{+3}\color{blue}{-3-4x } & = & -4 \color{red}{ +4x }\color{blue}{-3-4x } \\\Leftrightarrow & -x \color{blue}{-4x } & = & -4 \color{blue}{-3} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-1}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-1}\color{blue}{+1-x } & = & 1 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 1 \color{blue}{+1} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+13}& = & -5 \color{red}{ +8x } \\\Leftrightarrow & -13x \color{red}{+13}\color{blue}{-13-8x } & = & -5 \color{red}{ +8x }\color{blue}{-13-8x } \\\Leftrightarrow & -13x \color{blue}{-8x } & = & -5 \color{blue}{-13} \\\Leftrightarrow &-21x & = &-18\\\Leftrightarrow & \color{red}{-21}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-18}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-11}& = & -3 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-11}\color{blue}{+11+3x } & = & -3 \color{red}{ -3x }\color{blue}{+11+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -3 \color{blue}{+11} \\\Leftrightarrow &13x & = &8\\\Leftrightarrow & \color{red}{13}x & = &8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+5}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-x } & = & 11 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 11 \color{blue}{-5} \\\Leftrightarrow &-15x & = &6\\\Leftrightarrow & \color{red}{-15}x & = &6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+14}& = & 10 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+14}\color{blue}{-14+3x } & = & 10 \color{red}{ -3x }\color{blue}{-14+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 10 \color{blue}{-14} \\\Leftrightarrow &10x & = &-4\\\Leftrightarrow & \color{red}{10}x & = &-4\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-4}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)