Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{-1}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-1}\color{blue}{+1-5x } & = & 7 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 7 \color{blue}{+1} \\\Leftrightarrow &-9x & = &8\\\Leftrightarrow & \color{red}{-9}x & = &8\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{8}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+4}\color{blue}{-4-x } & = & 5 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 5 \color{blue}{-4} \\\Leftrightarrow &-4x & = &1\\\Leftrightarrow & \color{red}{-4}x & = &1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+15}& = & -4 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+15}\color{blue}{-15+4x } & = & -4 \color{red}{ -4x }\color{blue}{-15+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -4 \color{blue}{-15} \\\Leftrightarrow &9x & = &-19\\\Leftrightarrow & \color{red}{9}x & = &-19\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-19}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{9} } & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+13}& = & -9 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{+13}\color{blue}{-13-3x } & = & -9 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & -9 \color{blue}{-13} \\\Leftrightarrow &7x & = &-22\\\Leftrightarrow & \color{red}{7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-14}& = & 2 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14+14x } & = & 2 \color{red}{ -14x }\color{blue}{+14+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & 2 \color{blue}{+14} \\\Leftrightarrow &17x & = &16\\\Leftrightarrow & \color{red}{17}x & = &16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{16}{17} } & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+10}& = & 8 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10-4x } & = & 8 \color{red}{ +4x }\color{blue}{-10-4x } \\\Leftrightarrow & 11x \color{blue}{-4x } & = & 8 \color{blue}{-10} \\\Leftrightarrow &7x & = &-2\\\Leftrightarrow & \color{red}{7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-12}& = & -13 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-3x } & = & -13 \color{red}{ +3x }\color{blue}{+12-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & -13 \color{blue}{+12} \\\Leftrightarrow &-8x & = &-1\\\Leftrightarrow & \color{red}{-8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-5}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-x } & = & -7 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -7 \color{blue}{+5} \\\Leftrightarrow &-5x & = &-2\\\Leftrightarrow & \color{red}{-5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-8}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8-x } & = & -3 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -3 \color{blue}{+8} \\\Leftrightarrow &-9x & = &5\\\Leftrightarrow & \color{red}{-9}x & = &5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+9}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-x } & = & 15 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 15 \color{blue}{-9} \\\Leftrightarrow &-8x & = &6\\\Leftrightarrow & \color{red}{-8}x & = &6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-10}& = & -10 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{-10}\color{blue}{+10+3x } & = & -10 \color{red}{ -3x }\color{blue}{+10+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -10 \color{blue}{+10} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{-6}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-6}\color{blue}{+6-7x } & = & -9 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -9 \color{blue}{+6} \\\Leftrightarrow &3x & = &-3\\\Leftrightarrow & \color{red}{3}x & = &-3\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-3}{3} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)