Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+11}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+11}\color{blue}{-11-x } & = & -8 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &-4x & = &-19\\\Leftrightarrow & \color{red}{-4}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{19}{4} } & & \\ & V = \left\{ \frac{19}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+6}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+6}\color{blue}{-6-x } & = & 13 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 13 \color{blue}{-6} \\\Leftrightarrow &13x & = &7\\\Leftrightarrow & \color{red}{13}x & = &7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+1}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{+1}\color{blue}{-1-x } & = & -9 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -9 \color{blue}{-1} \\\Leftrightarrow &2x & = &-10\\\Leftrightarrow & \color{red}{2}x & = &-10\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-10}{2} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-x } & = & -8 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &-5x & = &-20\\\Leftrightarrow & \color{red}{-5}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-20}{-5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{-3}& = & -14 \color{red}{ -3x } \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3+3x } & = & -14 \color{red}{ -3x }\color{blue}{+3+3x } \\\Leftrightarrow & x \color{blue}{+3x } & = & -14 \color{blue}{+3} \\\Leftrightarrow &4x & = &-11\\\Leftrightarrow & \color{red}{4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-11}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{-6}& = & -9 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-3x } & = & -9 \color{red}{ +3x }\color{blue}{+6-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & -9 \color{blue}{+6} \\\Leftrightarrow &-17x & = &-3\\\Leftrightarrow & \color{red}{-17}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-1}& = & -6 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{-1}\color{blue}{+1-5x } & = & -6 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & 11x \color{blue}{-5x } & = & -6 \color{blue}{+1} \\\Leftrightarrow &6x & = &-5\\\Leftrightarrow & \color{red}{6}x & = &-5\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-5}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{-14}& = & -11 \color{red}{ -6x } \\\Leftrightarrow & x \color{red}{-14}\color{blue}{+14+6x } & = & -11 \color{red}{ -6x }\color{blue}{+14+6x } \\\Leftrightarrow & x \color{blue}{+6x } & = & -11 \color{blue}{+14} \\\Leftrightarrow &7x & = &3\\\Leftrightarrow & \color{red}{7}x & = &3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+7}& = & -8 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+7}\color{blue}{-7+15x } & = & -8 \color{red}{ -15x }\color{blue}{-7+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -8 \color{blue}{-7} \\\Leftrightarrow &19x & = &-15\\\Leftrightarrow & \color{red}{19}x & = &-15\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-15}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{19} } & & \\ & V = \left\{ \frac{-15}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-3}& = & 3 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{-3}\color{blue}{+3+15x } & = & 3 \color{red}{ -15x }\color{blue}{+3+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 3 \color{blue}{+3} \\\Leftrightarrow &19x & = &6\\\Leftrightarrow & \color{red}{19}x & = &6\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{6}{19} \\\Leftrightarrow & \color{green}{ x = \frac{6}{19} } & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-12}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-x } & = & -6 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -6 \color{blue}{+12} \\\Leftrightarrow &-7x & = &6\\\Leftrightarrow & \color{red}{-7}x & = &6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-9}& = & 12 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-14x } & = & 12 \color{red}{ +14x }\color{blue}{+9-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 12 \color{blue}{+9} \\\Leftrightarrow &-27x & = &21\\\Leftrightarrow & \color{red}{-27}x & = &21\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{21}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)