Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+12}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12-x } & = & -7 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -7 \color{blue}{-12} \\\Leftrightarrow &-9x & = &-19\\\Leftrightarrow & \color{red}{-9}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-19}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{19}{9} } & & \\ & V = \left\{ \frac{19}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-9}& = & 1 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-9}\color{blue}{+9-8x } & = & 1 \color{red}{ +8x }\color{blue}{+9-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & 1 \color{blue}{+9} \\\Leftrightarrow &-23x & = &10\\\Leftrightarrow & \color{red}{-23}x & = &10\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{10}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{23} } & & \\ & V = \left\{ \frac{-10}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-4}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-4}\color{blue}{+4-x } & = & 8 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &-7x & = &12\\\Leftrightarrow & \color{red}{-7}x & = &12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{+15}& = & -9 \color{red}{ -4x } \\\Leftrightarrow & x \color{red}{+15}\color{blue}{-15+4x } & = & -9 \color{red}{ -4x }\color{blue}{-15+4x } \\\Leftrightarrow & x \color{blue}{+4x } & = & -9 \color{blue}{-15} \\\Leftrightarrow &5x & = &-24\\\Leftrightarrow & \color{red}{5}x & = &-24\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-24}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{5} } & & \\ & V = \left\{ \frac{-24}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-10}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10+13x } & = & -3 \color{red}{ -13x }\color{blue}{+10+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -3 \color{blue}{+10} \\\Leftrightarrow &23x & = &7\\\Leftrightarrow & \color{red}{23}x & = &7\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{7}{23} \\\Leftrightarrow & \color{green}{ x = \frac{7}{23} } & & \\ & V = \left\{ \frac{7}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+13}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+13}\color{blue}{-13-x } & = & -12 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -12 \color{blue}{-13} \\\Leftrightarrow &-12x & = &-25\\\Leftrightarrow & \color{red}{-12}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-25}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{25}{12} } & & \\ & V = \left\{ \frac{25}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+9}& = & -6 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{+9}\color{blue}{-9-3x } & = & -6 \color{red}{ +3x }\color{blue}{-9-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & -6 \color{blue}{-9} \\\Leftrightarrow &7x & = &-15\\\Leftrightarrow & \color{red}{7}x & = &-15\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-15}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-6}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-x } & = & 6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 6 \color{blue}{+6} \\\Leftrightarrow &-15x & = &12\\\Leftrightarrow & \color{red}{-15}x & = &12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{-9}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-x } & = & 7 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 7 \color{blue}{+9} \\\Leftrightarrow &-4x & = &16\\\Leftrightarrow & \color{red}{-4}x & = &16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{16}{-4} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-7}& = & 2 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7+4x } & = & 2 \color{red}{ -4x }\color{blue}{+7+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 2 \color{blue}{+7} \\\Leftrightarrow &9x & = &9\\\Leftrightarrow & \color{red}{9}x & = &9\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{9}{9} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-14}& = & -10 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14+11x } & = & -10 \color{red}{ -11x }\color{blue}{+14+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -10 \color{blue}{+14} \\\Leftrightarrow &26x & = &4\\\Leftrightarrow & \color{red}{26}x & = &4\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{4}{26} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-6}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6-x } & = & -11 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & -11 \color{blue}{+6} \\\Leftrightarrow &4x & = &-5\\\Leftrightarrow & \color{red}{4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-5}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)