Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-14}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14-7x } & = & 4 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 4 \color{blue}{+14} \\\Leftrightarrow &3x & = &18\\\Leftrightarrow & \color{red}{3}x & = &18\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{18}{3} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+4}& = & -14 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4-5x } & = & -14 \color{red}{ +5x }\color{blue}{-4-5x } \\\Leftrightarrow & 11x \color{blue}{-5x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &6x & = &-18\\\Leftrightarrow & \color{red}{6}x & = &-18\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-18}{6} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+15}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+15}\color{blue}{-15-x } & = & -9 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -9 \color{blue}{-15} \\\Leftrightarrow &-7x & = &-24\\\Leftrightarrow & \color{red}{-7}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-24}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{24}{7} } & & \\ & V = \left\{ \frac{24}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{-2}& = & -5 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{-2}\color{blue}{+2+15x } & = & -5 \color{red}{ -15x }\color{blue}{+2+15x } \\\Leftrightarrow & -x \color{blue}{+15x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &14x & = &-3\\\Leftrightarrow & \color{red}{14}x & = &-3\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-3}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-2}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2-x } & = & -15 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -15 \color{blue}{+2} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+8}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8-7x } & = & 15 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & 15 \color{blue}{-8} \\\Leftrightarrow &-5x & = &7\\\Leftrightarrow & \color{red}{-5}x & = &7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+4}& = & -10 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+4}\color{blue}{-4+13x } & = & -10 \color{red}{ -13x }\color{blue}{-4+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -10 \color{blue}{-4} \\\Leftrightarrow &22x & = &-14\\\Leftrightarrow & \color{red}{22}x & = &-14\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-14}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-12}& = & -9 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12+11x } & = & -9 \color{red}{ -11x }\color{blue}{+12+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -9 \color{blue}{+12} \\\Leftrightarrow &17x & = &3\\\Leftrightarrow & \color{red}{17}x & = &3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{-11}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11-x } & = & -8 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -8 \color{blue}{+11} \\\Leftrightarrow &-4x & = &3\\\Leftrightarrow & \color{red}{-4}x & = &3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-5}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-x } & = & 15 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 15 \color{blue}{+5} \\\Leftrightarrow &-9x & = &20\\\Leftrightarrow & \color{red}{-9}x & = &20\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{20}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{9} } & & \\ & V = \left\{ \frac{-20}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-7}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7-x } & = & 9 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 9 \color{blue}{+7} \\\Leftrightarrow &13x & = &16\\\Leftrightarrow & \color{red}{13}x & = &16\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{16}{13} \\\Leftrightarrow & \color{green}{ x = \frac{16}{13} } & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-15}& = & 6 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{-15}\color{blue}{+15-5x } & = & 6 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & 6 \color{blue}{+15} \\\Leftrightarrow &-x & = &21\\\Leftrightarrow & \color{red}{-}x & = &21\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{21}{-1} \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)