Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-6}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x } & = & 13 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 13 \color{blue}{+6} \\\Leftrightarrow &-4x & = &19\\\Leftrightarrow & \color{red}{-4}x & = &19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{4} } & & \\ & V = \left\{ \frac{-19}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-3}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & 3x \color{red}{-3}\color{blue}{+3-11x } & = & -8 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & 3x \color{blue}{-11x } & = & -8 \color{blue}{+3} \\\Leftrightarrow &-8x & = &-5\\\Leftrightarrow & \color{red}{-8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+1}& = & 11 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+1}\color{blue}{-1+9x } & = & 11 \color{red}{ -9x }\color{blue}{-1+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 11 \color{blue}{-1} \\\Leftrightarrow &19x & = &10\\\Leftrightarrow & \color{red}{19}x & = &10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{10}{19} } & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+12}& = & 6 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12-14x } & = & 6 \color{red}{ +14x }\color{blue}{-12-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & 6 \color{blue}{-12} \\\Leftrightarrow &-x & = &-6\\\Leftrightarrow & \color{red}{-}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-6}{-1} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+11}& = & -5 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11-3x } & = & -5 \color{red}{ +3x }\color{blue}{-11-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & -5 \color{blue}{-11} \\\Leftrightarrow &-8x & = &-16\\\Leftrightarrow & \color{red}{-8}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-16}{-8} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-7}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7-x } & = & -14 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -14 \color{blue}{+7} \\\Leftrightarrow &-4x & = &-7\\\Leftrightarrow & \color{red}{-4}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-1}& = & -6 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1+9x } & = & -6 \color{red}{ -9x }\color{blue}{+1+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & -6 \color{blue}{+1} \\\Leftrightarrow &8x & = &-5\\\Leftrightarrow & \color{red}{8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-5}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{-6}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-6}\color{blue}{+6-x } & = & 8 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 8 \color{blue}{+6} \\\Leftrightarrow &x & = &14\\\Leftrightarrow & \color{red}{}x & = &14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 14 \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-7}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-7}\color{blue}{+7-x } & = & 9 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 9 \color{blue}{+7} \\\Leftrightarrow &5x & = &16\\\Leftrightarrow & \color{red}{5}x & = &16\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{16}{5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{-7}& = & 1 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-7}\color{blue}{+7+14x } & = & 1 \color{red}{ -14x }\color{blue}{+7+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 1 \color{blue}{+7} \\\Leftrightarrow &29x & = &8\\\Leftrightarrow & \color{red}{29}x & = &8\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{8}{29} \\\Leftrightarrow & \color{green}{ x = \frac{8}{29} } & & \\ & V = \left\{ \frac{8}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+14}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+14}\color{blue}{-14-x } & = & -3 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &-15x & = &-17\\\Leftrightarrow & \color{red}{-15}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{17}{15} } & & \\ & V = \left\{ \frac{17}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+1}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+1}\color{blue}{-1-7x } & = & -7 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -7 \color{blue}{-1} \\\Leftrightarrow &-5x & = &-8\\\Leftrightarrow & \color{red}{-5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)