Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+9}\color{blue}{-9-x } & = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+2}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2-x } & = & 6 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 6 \color{blue}{-2} \\\Leftrightarrow &-7x & = &4\\\Leftrightarrow & \color{red}{-7}x & = &4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{-1}& = & 10 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1-6x } & = & 10 \color{red}{ +6x }\color{blue}{+1-6x } \\\Leftrightarrow & x \color{blue}{-6x } & = & 10 \color{blue}{+1} \\\Leftrightarrow &-5x & = &11\\\Leftrightarrow & \color{red}{-5}x & = &11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-13}& = & 1 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13+2x } & = & 1 \color{red}{ -2x }\color{blue}{+13+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & 1 \color{blue}{+13} \\\Leftrightarrow &7x & = &14\\\Leftrightarrow & \color{red}{7}x & = &14\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{14}{7} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{+13}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13-x } & = & -14 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & -14 \color{blue}{-13} \\\Leftrightarrow &10x & = &-27\\\Leftrightarrow & \color{red}{10}x & = &-27\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-27}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{10} } & & \\ & V = \left\{ \frac{-27}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+13}& = & -10 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{+13}\color{blue}{-13+15x } & = & -10 \color{red}{ -15x }\color{blue}{-13+15x } \\\Leftrightarrow & -x \color{blue}{+15x } & = & -10 \color{blue}{-13} \\\Leftrightarrow &14x & = &-23\\\Leftrightarrow & \color{red}{14}x & = &-23\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-23}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{14} } & & \\ & V = \left\{ \frac{-23}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+11}& = & -2 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11+7x } & = & -2 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -2 \color{blue}{-11} \\\Leftrightarrow &22x & = &-13\\\Leftrightarrow & \color{red}{22}x & = &-13\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-13}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{22} } & & \\ & V = \left\{ \frac{-13}{22} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2-x } & = & -3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &5x & = &-5\\\Leftrightarrow & \color{red}{5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-5}{5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+1}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1-x } & = & 8 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 8 \color{blue}{-1} \\\Leftrightarrow &-7x & = &7\\\Leftrightarrow & \color{red}{-7}x & = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-15}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-15}\color{blue}{+15-x } & = & -13 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -13 \color{blue}{+15} \\\Leftrightarrow &-15x & = &2\\\Leftrightarrow & \color{red}{-15}x & = &2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{-2}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-2}\color{blue}{+2-x } & = & -1 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -1 \color{blue}{+2} \\\Leftrightarrow &-10x & = &1\\\Leftrightarrow & \color{red}{-10}x & = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+10}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10-x } & = & -15 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -15 \color{blue}{-10} \\\Leftrightarrow &8x & = &-25\\\Leftrightarrow & \color{red}{8}x & = &-25\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-25}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{8} } & & \\ & V = \left\{ \frac{-25}{8} \right\} & \\\end{align}\)