Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-8}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-8}\color{blue}{+8-5x } & = & 14 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 14 \color{blue}{+8} \\\Leftrightarrow &-17x & = &22\\\Leftrightarrow & \color{red}{-17}x & = &22\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{22}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{17} } & & \\ & V = \left\{ \frac{-22}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-11}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11-5x } & = & -4 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & 11x \color{blue}{-5x } & = & -4 \color{blue}{+11} \\\Leftrightarrow &6x & = &7\\\Leftrightarrow & \color{red}{6}x & = &7\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{7}{6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+15}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+15}\color{blue}{-15-x } & = & -11 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -11 \color{blue}{-15} \\\Leftrightarrow &13x & = &-26\\\Leftrightarrow & \color{red}{13}x & = &-26\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-26}{13} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-12}& = & 6 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12+7x } & = & 6 \color{red}{ -7x }\color{blue}{+12+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 6 \color{blue}{+12} \\\Leftrightarrow &22x & = &18\\\Leftrightarrow & \color{red}{22}x & = &18\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{18}{22} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+15}& = & -5 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15+11x } & = & -5 \color{red}{ -11x }\color{blue}{-15+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -5 \color{blue}{-15} \\\Leftrightarrow &15x & = &-20\\\Leftrightarrow & \color{red}{15}x & = &-20\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-20}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+1}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+1}\color{blue}{-1-7x } & = & 15 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 15 \color{blue}{-1} \\\Leftrightarrow &-17x & = &14\\\Leftrightarrow & \color{red}{-17}x & = &14\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{14}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{17} } & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-3}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3-x } & = & 6 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 6 \color{blue}{+3} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-14}& = & 6 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14-12x } & = & 6 \color{red}{ +12x }\color{blue}{+14-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & 6 \color{blue}{+14} \\\Leftrightarrow &-x & = &20\\\Leftrightarrow & \color{red}{-}x & = &20\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{20}{-1} \\\Leftrightarrow & \color{green}{ x = -20 } & & \\ & V = \left\{ -20 \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-7}& = & 6 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7+6x } & = & 6 \color{red}{ -6x }\color{blue}{+7+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 6 \color{blue}{+7} \\\Leftrightarrow &19x & = &13\\\Leftrightarrow & \color{red}{19}x & = &13\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{13}{19} \\\Leftrightarrow & \color{green}{ x = \frac{13}{19} } & & \\ & V = \left\{ \frac{13}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{+8}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+8}\color{blue}{-8-x } & = & 6 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 6 \color{blue}{-8} \\\Leftrightarrow &-14x & = &-2\\\Leftrightarrow & \color{red}{-14}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+4}& = & 9 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+4}\color{blue}{-4+11x } & = & 9 \color{red}{ -11x }\color{blue}{-4+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & 9 \color{blue}{-4} \\\Leftrightarrow &14x & = &5\\\Leftrightarrow & \color{red}{14}x & = &5\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{5}{14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+4}& = & 4 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+4}\color{blue}{-4+3x } & = & 4 \color{red}{ -3x }\color{blue}{-4+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 4 \color{blue}{-4} \\\Leftrightarrow &13x & = &0\\\Leftrightarrow & \color{red}{13}x & = &0\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{0}{13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)