Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-2}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2-x } & = & -4 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -4 \color{blue}{+2} \\\Leftrightarrow &-8x & = &-2\\\Leftrightarrow & \color{red}{-8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+13}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+13}\color{blue}{-13-x } & = & 13 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 13 \color{blue}{-13} \\\Leftrightarrow &-10x & = &0\\\Leftrightarrow & \color{red}{-10}x & = &0\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{0}{-10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+11}& = & -9 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11+3x } & = & -9 \color{red}{ -3x }\color{blue}{-11+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -9 \color{blue}{-11} \\\Leftrightarrow &7x & = &-20\\\Leftrightarrow & \color{red}{7}x & = &-20\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-20}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{7} } & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+4}& = & -7 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4+14x } & = & -7 \color{red}{ -14x }\color{blue}{-4+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &29x & = &-11\\\Leftrightarrow & \color{red}{29}x & = &-11\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-11}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{29} } & & \\ & V = \left\{ \frac{-11}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-3}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3-9x } & = & -10 \color{red}{ +9x }\color{blue}{+3-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &-20x & = &-7\\\Leftrightarrow & \color{red}{-20}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-7}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{7}{20} } & & \\ & V = \left\{ \frac{7}{20} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-15}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-x } & = & 9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 9 \color{blue}{+15} \\\Leftrightarrow &-12x & = &24\\\Leftrightarrow & \color{red}{-12}x & = &24\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{24}{-12} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{-11}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11-x } & = & 9 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 9 \color{blue}{+11} \\\Leftrightarrow &-16x & = &20\\\Leftrightarrow & \color{red}{-16}x & = &20\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{20}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+14}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+14}\color{blue}{-14+11x } & = & -7 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -7 \color{blue}{-14} \\\Leftrightarrow &23x & = &-21\\\Leftrightarrow & \color{red}{23}x & = &-21\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-21}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{23} } & & \\ & V = \left\{ \frac{-21}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-12}& = & 1 \color{red}{ +14x } \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12-14x } & = & 1 \color{red}{ +14x }\color{blue}{+12-14x } \\\Leftrightarrow & 9x \color{blue}{-14x } & = & 1 \color{blue}{+12} \\\Leftrightarrow &-5x & = &13\\\Leftrightarrow & \color{red}{-5}x & = &13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+6}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+6}\color{blue}{-6-x } & = & -1 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -1 \color{blue}{-6} \\\Leftrightarrow &5x & = &-7\\\Leftrightarrow & \color{red}{5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{-8}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{-8}\color{blue}{+8-11x } & = & -9 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & -9 \color{blue}{+8} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{+12}& = & 14 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12+7x } & = & 14 \color{red}{ -7x }\color{blue}{-12+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 14 \color{blue}{-12} \\\Leftrightarrow &19x & = &2\\\Leftrightarrow & \color{red}{19}x & = &2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{2}{19} } & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)