Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-8}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8-x } & = & 11 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 11 \color{blue}{+8} \\\Leftrightarrow &-10x & = &19\\\Leftrightarrow & \color{red}{-10}x & = &19\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{19}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{10} } & & \\ & V = \left\{ \frac{-19}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+13}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+13}\color{blue}{-13-11x } & = & 5 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 5 \color{blue}{-13} \\\Leftrightarrow &-9x & = &-8\\\Leftrightarrow & \color{red}{-9}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-8}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{9} } & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-2}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-2}\color{blue}{+2-x } & = & -4 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -4 \color{blue}{+2} \\\Leftrightarrow &-3x & = &-2\\\Leftrightarrow & \color{red}{-3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{-2}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-2}\color{blue}{+2-x } & = & -2 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -2 \color{blue}{+2} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+14}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14-x } & = & 5 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 5 \color{blue}{-14} \\\Leftrightarrow &-7x & = &-9\\\Leftrightarrow & \color{red}{-7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-12}& = & -6 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-12}\color{blue}{+12+7x } & = & -6 \color{red}{ -7x }\color{blue}{+12+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -6 \color{blue}{+12} \\\Leftrightarrow &15x & = &6\\\Leftrightarrow & \color{red}{15}x & = &6\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{6}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+2}& = & 13 \color{red}{ +11x } \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2-11x } & = & 13 \color{red}{ +11x }\color{blue}{-2-11x } \\\Leftrightarrow & -x \color{blue}{-11x } & = & 13 \color{blue}{-2} \\\Leftrightarrow &-12x & = &11\\\Leftrightarrow & \color{red}{-12}x & = &11\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{11}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{12} } & & \\ & V = \left\{ \frac{-11}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-15}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15-x } & = & -9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -9 \color{blue}{+15} \\\Leftrightarrow &-11x & = &6\\\Leftrightarrow & \color{red}{-11}x & = &6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-9}& = & 1 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9+3x } & = & 1 \color{red}{ -3x }\color{blue}{+9+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 1 \color{blue}{+9} \\\Leftrightarrow &13x & = &10\\\Leftrightarrow & \color{red}{13}x & = &10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+14}& = & 12 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14+8x } & = & 12 \color{red}{ -8x }\color{blue}{-14+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 12 \color{blue}{-14} \\\Leftrightarrow &19x & = &-2\\\Leftrightarrow & \color{red}{19}x & = &-2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{19} } & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+5}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-3x } & = & -11 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & -11 \color{blue}{-5} \\\Leftrightarrow &-14x & = &-16\\\Leftrightarrow & \color{red}{-14}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-16}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-14}& = & 15 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14+15x } & = & 15 \color{red}{ -15x }\color{blue}{+14+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 15 \color{blue}{+14} \\\Leftrightarrow &19x & = &29\\\Leftrightarrow & \color{red}{19}x & = &29\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{29}{19} \\\Leftrightarrow & \color{green}{ x = \frac{29}{19} } & & \\ & V = \left\{ \frac{29}{19} \right\} & \\\end{align}\)