Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+8}& = & -14 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8+13x } & = & -14 \color{red}{ -13x }\color{blue}{-8+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -14 \color{blue}{-8} \\\Leftrightarrow &24x & = &-22\\\Leftrightarrow & \color{red}{24}x & = &-22\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-22}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{12} } & & \\ & V = \left\{ \frac{-11}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+9}& = & 9 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9+7x } & = & 9 \color{red}{ -7x }\color{blue}{-9+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &22x & = &0\\\Leftrightarrow & \color{red}{22}x & = &0\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{0}{22} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+13}& = & -5 \color{red}{ +4x } \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13-4x } & = & -5 \color{red}{ +4x }\color{blue}{-13-4x } \\\Leftrightarrow & x \color{blue}{-4x } & = & -5 \color{blue}{-13} \\\Leftrightarrow &-3x & = &-18\\\Leftrightarrow & \color{red}{-3}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-18}{-3} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-13}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13-11x } & = & 4 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & 3x \color{blue}{-11x } & = & 4 \color{blue}{+13} \\\Leftrightarrow &-8x & = &17\\\Leftrightarrow & \color{red}{-8}x & = &17\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{17}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{8} } & & \\ & V = \left\{ \frac{-17}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-14}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14-x } & = & -6 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -6 \color{blue}{+14} \\\Leftrightarrow &x & = &8\\\Leftrightarrow & \color{red}{}x & = &8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 8 \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+2}\color{blue}{-2-x } & = & -3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &11x & = &-5\\\Leftrightarrow & \color{red}{11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-13}& = & -11 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13-9x } & = & -11 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -11 \color{blue}{+13} \\\Leftrightarrow &-13x & = &2\\\Leftrightarrow & \color{red}{-13}x & = &2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-13}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-9x } & = & 3 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & 3 \color{blue}{+13} \\\Leftrightarrow &-20x & = &16\\\Leftrightarrow & \color{red}{-20}x & = &16\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{16}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{+8}& = & 7 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+8}\color{blue}{-8-6x } & = & 7 \color{red}{ +6x }\color{blue}{-8-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 7 \color{blue}{-8} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-1}& = & 6 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{-1}\color{blue}{+1-6x } & = & 6 \color{red}{ +6x }\color{blue}{+1-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & 6 \color{blue}{+1} \\\Leftrightarrow &-x & = &7\\\Leftrightarrow & \color{red}{-}x & = &7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{7}{-1} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{+4}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-x } & = & 6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 6 \color{blue}{-4} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+2}& = & -4 \color{red}{ +2x } \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2-2x } & = & -4 \color{red}{ +2x }\color{blue}{-2-2x } \\\Leftrightarrow & 11x \color{blue}{-2x } & = & -4 \color{blue}{-2} \\\Leftrightarrow &9x & = &-6\\\Leftrightarrow & \color{red}{9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)