Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-4}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-4}\color{blue}{+4-x } & = & 6 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 6 \color{blue}{+4} \\\Leftrightarrow &-12x & = &10\\\Leftrightarrow & \color{red}{-12}x & = &10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-15}& = & -8 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15+3x } & = & -8 \color{red}{ -3x }\color{blue}{+15+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -8 \color{blue}{+15} \\\Leftrightarrow &10x & = &7\\\Leftrightarrow & \color{red}{10}x & = &7\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{7}{10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-13}& = & 2 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{-13}\color{blue}{+13-4x } & = & 2 \color{red}{ +4x }\color{blue}{+13-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & 2 \color{blue}{+13} \\\Leftrightarrow &5x & = &15\\\Leftrightarrow & \color{red}{5}x & = &15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{15}{5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{+7}& = & 6 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+7}\color{blue}{-7-8x } & = & 6 \color{red}{ +8x }\color{blue}{-7-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & 6 \color{blue}{-7} \\\Leftrightarrow &-23x & = &-1\\\Leftrightarrow & \color{red}{-23}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-1}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{1}{23} } & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+13}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-x } & = & 11 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 11 \color{blue}{-13} \\\Leftrightarrow &-7x & = &-2\\\Leftrightarrow & \color{red}{-7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+13}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-x } & = & -7 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -7 \color{blue}{-13} \\\Leftrightarrow &-13x & = &-20\\\Leftrightarrow & \color{red}{-13}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-20}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{20}{13} } & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-1}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-1}\color{blue}{+1-x } & = & 7 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 7 \color{blue}{+1} \\\Leftrightarrow &-5x & = &8\\\Leftrightarrow & \color{red}{-5}x & = &8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{-5}& = & -5 \color{red}{ -12x } \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5+12x } & = & -5 \color{red}{ -12x }\color{blue}{+5+12x } \\\Leftrightarrow & -x \color{blue}{+12x } & = & -5 \color{blue}{+5} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+13}& = & -4 \color{red}{ +8x } \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13-8x } & = & -4 \color{red}{ +8x }\color{blue}{-13-8x } \\\Leftrightarrow & 13x \color{blue}{-8x } & = & -4 \color{blue}{-13} \\\Leftrightarrow &5x & = &-17\\\Leftrightarrow & \color{red}{5}x & = &-17\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-17}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{5} } & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-14}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14-x } & = & -13 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -13 \color{blue}{+14} \\\Leftrightarrow &-15x & = &1\\\Leftrightarrow & \color{red}{-15}x & = &1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+12}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12-7x } & = & -8 \color{red}{ +7x }\color{blue}{-12-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &-x & = &-20\\\Leftrightarrow & \color{red}{-}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-20}{-1} \\\Leftrightarrow & \color{green}{ x = 20 } & & \\ & V = \left\{ 20 \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{+3}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3-x } & = & 13 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 13 \color{blue}{-3} \\\Leftrightarrow &-13x & = &10\\\Leftrightarrow & \color{red}{-13}x & = &10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)