Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+14}& = & 12 \color{red}{ -5x } \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14+5x } & = & 12 \color{red}{ -5x }\color{blue}{-14+5x } \\\Leftrightarrow & x \color{blue}{+5x } & = & 12 \color{blue}{-14} \\\Leftrightarrow &6x & = &-2\\\Leftrightarrow & \color{red}{6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-2}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-11}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-x } & = & 6 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 6 \color{blue}{+11} \\\Leftrightarrow &-5x & = &17\\\Leftrightarrow & \color{red}{-5}x & = &17\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{17}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{5} } & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{+8}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+8}\color{blue}{-8-x } & = & -14 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -14 \color{blue}{-8} \\\Leftrightarrow &-4x & = &-22\\\Leftrightarrow & \color{red}{-4}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-22}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+11}& = & 10 \color{red}{ +14x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11-14x } & = & 10 \color{red}{ +14x }\color{blue}{-11-14x } \\\Leftrightarrow & 3x \color{blue}{-14x } & = & 10 \color{blue}{-11} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+8}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8-7x } & = & -11 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & -11 \color{blue}{-8} \\\Leftrightarrow &-x & = &-19\\\Leftrightarrow & \color{red}{-}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-19}{-1} \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-6}& = & 2 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6+13x } & = & 2 \color{red}{ -13x }\color{blue}{+6+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 2 \color{blue}{+6} \\\Leftrightarrow &20x & = &8\\\Leftrightarrow & \color{red}{20}x & = &8\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{8}{20} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+7}& = & 5 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7-6x } & = & 5 \color{red}{ +6x }\color{blue}{-7-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 5 \color{blue}{-7} \\\Leftrightarrow &-11x & = &-2\\\Leftrightarrow & \color{red}{-11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{+3}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-7x } & = & 9 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 9 \color{blue}{-3} \\\Leftrightarrow &-13x & = &6\\\Leftrightarrow & \color{red}{-13}x & = &6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-9}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9-9x } & = & 8 \color{red}{ +9x }\color{blue}{+9-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & 8 \color{blue}{+9} \\\Leftrightarrow &-x & = &17\\\Leftrightarrow & \color{red}{-}x & = &17\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{17}{-1} \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+10}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+10}\color{blue}{-10-x } & = & 9 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 9 \color{blue}{-10} \\\Leftrightarrow &x & = &-1\\\Leftrightarrow & \color{red}{}x & = &-1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -1 \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{+2}& = & -3 \color{red}{ -9x } \\\Leftrightarrow & 7x \color{red}{+2}\color{blue}{-2+9x } & = & -3 \color{red}{ -9x }\color{blue}{-2+9x } \\\Leftrightarrow & 7x \color{blue}{+9x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &16x & = &-5\\\Leftrightarrow & \color{red}{16}x & = &-5\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-5}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{16} } & & \\ & V = \left\{ \frac{-5}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-9}& = & -13 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-9}\color{blue}{+9-11x } & = & -13 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -13 \color{blue}{+9} \\\Leftrightarrow &-5x & = &-4\\\Leftrightarrow & \color{red}{-5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)