Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-5}& = & 9 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-5}\color{blue}{+5-14x } & = & 9 \color{red}{ +14x }\color{blue}{+5-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 9 \color{blue}{+5} \\\Leftrightarrow &-25x & = &14\\\Leftrightarrow & \color{red}{-25}x & = &14\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{14}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{25} } & & \\ & V = \left\{ \frac{-14}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+1}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1-x } & = & -12 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -12 \color{blue}{-1} \\\Leftrightarrow &-9x & = &-13\\\Leftrightarrow & \color{red}{-9}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{-9}& = & -2 \color{red}{ +10x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9-10x } & = & -2 \color{red}{ +10x }\color{blue}{+9-10x } \\\Leftrightarrow & x \color{blue}{-10x } & = & -2 \color{blue}{+9} \\\Leftrightarrow &-9x & = &7\\\Leftrightarrow & \color{red}{-9}x & = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+1}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1-x } & = & -15 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -15 \color{blue}{-1} \\\Leftrightarrow &5x & = &-16\\\Leftrightarrow & \color{red}{5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-16}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{-10}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10-13x } & = & -10 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -10 \color{blue}{+10} \\\Leftrightarrow &-19x & = &0\\\Leftrightarrow & \color{red}{-19}x & = &0\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{0}{-19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+4}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4-13x } & = & -4 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & -4 \color{blue}{-4} \\\Leftrightarrow &-5x & = &-8\\\Leftrightarrow & \color{red}{-5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-6}& = & -4 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6-11x } & = & -4 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & -4 \color{blue}{+6} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-9}& = & 8 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9+11x } & = & 8 \color{red}{ -11x }\color{blue}{+9+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 8 \color{blue}{+9} \\\Leftrightarrow &23x & = &17\\\Leftrightarrow & \color{red}{23}x & = &17\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{17}{23} \\\Leftrightarrow & \color{green}{ x = \frac{17}{23} } & & \\ & V = \left\{ \frac{17}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-8}& = & 9 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8-5x } & = & 9 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 9 \color{blue}{+8} \\\Leftrightarrow &7x & = &17\\\Leftrightarrow & \color{red}{7}x & = &17\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{17}{7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{+5}& = & 1 \color{red}{ -7x } \\\Leftrightarrow & x \color{red}{+5}\color{blue}{-5+7x } & = & 1 \color{red}{ -7x }\color{blue}{-5+7x } \\\Leftrightarrow & x \color{blue}{+7x } & = & 1 \color{blue}{-5} \\\Leftrightarrow &8x & = &-4\\\Leftrightarrow & \color{red}{8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-13}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13-x } & = & -3 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -3 \color{blue}{+13} \\\Leftrightarrow &-14x & = &10\\\Leftrightarrow & \color{red}{-14}x & = &10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{+14}& = & 14 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{+14}\color{blue}{-14-3x } & = & 14 \color{red}{ +3x }\color{blue}{-14-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)