Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{-11}& = & -13 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-5x } & = & -13 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -13 \color{blue}{+11} \\\Leftrightarrow &-9x & = &-2\\\Leftrightarrow & \color{red}{-9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+13}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+13}\color{blue}{-13-x } & = & -5 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -5 \color{blue}{-13} \\\Leftrightarrow &13x & = &-18\\\Leftrightarrow & \color{red}{13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-18}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{13} } & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-7}& = & 1 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-7}\color{blue}{+7-11x } & = & 1 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 1 \color{blue}{+7} \\\Leftrightarrow &-18x & = &8\\\Leftrightarrow & \color{red}{-18}x & = &8\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{8}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-13}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-x } & = & -4 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -4 \color{blue}{+13} \\\Leftrightarrow &-12x & = &9\\\Leftrightarrow & \color{red}{-12}x & = &9\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{9}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+15}& = & 13 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15+7x } & = & 13 \color{red}{ -7x }\color{blue}{-15+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 13 \color{blue}{-15} \\\Leftrightarrow &11x & = &-2\\\Leftrightarrow & \color{red}{11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{-6}& = & 15 \color{red}{ +3x } \\\Leftrightarrow & 11x \color{red}{-6}\color{blue}{+6-3x } & = & 15 \color{red}{ +3x }\color{blue}{+6-3x } \\\Leftrightarrow & 11x \color{blue}{-3x } & = & 15 \color{blue}{+6} \\\Leftrightarrow &8x & = &21\\\Leftrightarrow & \color{red}{8}x & = &21\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{21}{8} \\\Leftrightarrow & \color{green}{ x = \frac{21}{8} } & & \\ & V = \left\{ \frac{21}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+14}& = & -14 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14+5x } & = & -14 \color{red}{ -5x }\color{blue}{-14+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -14 \color{blue}{-14} \\\Leftrightarrow &8x & = &-28\\\Leftrightarrow & \color{red}{8}x & = &-28\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-28}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-11}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11-x } & = & -6 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -6 \color{blue}{+11} \\\Leftrightarrow &-9x & = &5\\\Leftrightarrow & \color{red}{-9}x & = &5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-3}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3-x } & = & 13 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & 13 \color{blue}{+3} \\\Leftrightarrow &8x & = &16\\\Leftrightarrow & \color{red}{8}x & = &16\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{16}{8} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-2}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-2}\color{blue}{+2-x } & = & 8 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 8 \color{blue}{+2} \\\Leftrightarrow &-5x & = &10\\\Leftrightarrow & \color{red}{-5}x & = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+2}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & -7x \color{red}{+2}\color{blue}{-2-5x } & = & -2 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & -7x \color{blue}{-5x } & = & -2 \color{blue}{-2} \\\Leftrightarrow &-12x & = &-4\\\Leftrightarrow & \color{red}{-12}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{+2}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+2}\color{blue}{-2-5x } & = & -7 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -7 \color{blue}{-2} \\\Leftrightarrow &7x & = &-9\\\Leftrightarrow & \color{red}{7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)