Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-11}& = & 11 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-14x } & = & 11 \color{red}{ +14x }\color{blue}{+11-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 11 \color{blue}{+11} \\\Leftrightarrow &-25x & = &22\\\Leftrightarrow & \color{red}{-25}x & = &22\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{22}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{25} } & & \\ & V = \left\{ \frac{-22}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{-2}& = & 15 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2+9x } & = & 15 \color{red}{ -9x }\color{blue}{+2+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 15 \color{blue}{+2} \\\Leftrightarrow &19x & = &17\\\Leftrightarrow & \color{red}{19}x & = &17\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{17}{19} \\\Leftrightarrow & \color{green}{ x = \frac{17}{19} } & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{+4}& = & -6 \color{red}{ -4x } \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4+4x } & = & -6 \color{red}{ -4x }\color{blue}{-4+4x } \\\Leftrightarrow & -x \color{blue}{+4x } & = & -6 \color{blue}{-4} \\\Leftrightarrow &3x & = &-10\\\Leftrightarrow & \color{red}{3}x & = &-10\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-10}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+8}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+8}\color{blue}{-8-5x } & = & -4 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & -4 \color{blue}{-8} \\\Leftrightarrow &9x & = &-12\\\Leftrightarrow & \color{red}{9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-12}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+3}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-x } & = & 12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 12 \color{blue}{-3} \\\Leftrightarrow &-7x & = &9\\\Leftrightarrow & \color{red}{-7}x & = &9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-6}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-6}\color{blue}{+6-x } & = & -1 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -1 \color{blue}{+6} \\\Leftrightarrow &-9x & = &5\\\Leftrightarrow & \color{red}{-9}x & = &5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+9}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & 7x \color{red}{+9}\color{blue}{-9-13x } & = & -7 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & 7x \color{blue}{-13x } & = & -7 \color{blue}{-9} \\\Leftrightarrow &-6x & = &-16\\\Leftrightarrow & \color{red}{-6}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-16}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+5}& = & 4 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5-9x } & = & 4 \color{red}{ +9x }\color{blue}{-5-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+10}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+10}\color{blue}{-10-x } & = & -9 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -9 \color{blue}{-10} \\\Leftrightarrow &-7x & = &-19\\\Leftrightarrow & \color{red}{-7}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{19}{7} } & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+6}& = & -1 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6+4x } & = & -1 \color{red}{ -4x }\color{blue}{-6+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -1 \color{blue}{-6} \\\Leftrightarrow &9x & = &-7\\\Leftrightarrow & \color{red}{9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-7}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-13}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13-x } & = & -12 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -12 \color{blue}{+13} \\\Leftrightarrow &-8x & = &1\\\Leftrightarrow & \color{red}{-8}x & = &1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-12}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-12}\color{blue}{+12-x } & = & 2 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &-11x & = &14\\\Leftrightarrow & \color{red}{-11}x & = &14\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{14}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)