Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{+13}& = & 9 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{+13}\color{blue}{-13-9x } & = & 9 \color{red}{ +9x }\color{blue}{-13-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & 9 \color{blue}{-13} \\\Leftrightarrow &-11x & = &-4\\\Leftrightarrow & \color{red}{-11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{-9}& = & -1 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9+3x } & = & -1 \color{red}{ -3x }\color{blue}{+9+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -1 \color{blue}{+9} \\\Leftrightarrow &13x & = &8\\\Leftrightarrow & \color{red}{13}x & = &8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+1}& = & -3 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1-3x } & = & -3 \color{red}{ +3x }\color{blue}{-1-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & -3 \color{blue}{-1} \\\Leftrightarrow &x & = &-4\\\Leftrightarrow & \color{red}{}x & = &-4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -4 \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+3}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3-x } & = & 7 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 7 \color{blue}{-3} \\\Leftrightarrow &-12x & = &4\\\Leftrightarrow & \color{red}{-12}x & = &4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-4}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-4}\color{blue}{+4-x } & = & 4 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 4 \color{blue}{+4} \\\Leftrightarrow &-6x & = &8\\\Leftrightarrow & \color{red}{-6}x & = &8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{-3}& = & -14 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3+5x } & = & -14 \color{red}{ -5x }\color{blue}{+3+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -14 \color{blue}{+3} \\\Leftrightarrow &16x & = &-11\\\Leftrightarrow & \color{red}{16}x & = &-11\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-11}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{16} } & & \\ & V = \left\{ \frac{-11}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-14}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14-x } & = & 2 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 2 \color{blue}{+14} \\\Leftrightarrow &-9x & = &16\\\Leftrightarrow & \color{red}{-9}x & = &16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{9} } & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-10}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10-11x } & = & 6 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 6 \color{blue}{+10} \\\Leftrightarrow &x & = &16\\\Leftrightarrow & \color{red}{}x & = &16\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 16 \\\Leftrightarrow & \color{green}{ x = 16 } & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{+5}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5-7x } & = & 13 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & 13 \color{blue}{-5} \\\Leftrightarrow &-4x & = &8\\\Leftrightarrow & \color{red}{-4}x & = &8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{8}{-4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{-9}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-x } & = & 5 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 5 \color{blue}{+9} \\\Leftrightarrow &-10x & = &14\\\Leftrightarrow & \color{red}{-10}x & = &14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+14}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-x } & = & 7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 7 \color{blue}{-14} \\\Leftrightarrow &-14x & = &-7\\\Leftrightarrow & \color{red}{-14}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-7}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+3}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & 7x \color{red}{+3}\color{blue}{-3-5x } & = & -15 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 7x \color{blue}{-5x } & = & -15 \color{blue}{-3} \\\Leftrightarrow &2x & = &-18\\\Leftrightarrow & \color{red}{2}x & = &-18\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-18}{2} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)