Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+14}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-x } & = & 14 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+6}& = & -3 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+6}\color{blue}{-6+11x } & = & -3 \color{red}{ -11x }\color{blue}{-6+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &17x & = &-9\\\Leftrightarrow & \color{red}{17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-9}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{17} } & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-15}& = & -7 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-11x } & = & -7 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -7 \color{blue}{+15} \\\Leftrightarrow &-18x & = &8\\\Leftrightarrow & \color{red}{-18}x & = &8\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{8}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-14}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14-x } & = & 7 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 7 \color{blue}{+14} \\\Leftrightarrow &-14x & = &21\\\Leftrightarrow & \color{red}{-14}x & = &21\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{21}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-13}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13-x } & = & 2 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 2 \color{blue}{+13} \\\Leftrightarrow &-8x & = &15\\\Leftrightarrow & \color{red}{-8}x & = &15\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{15}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{8} } & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+15}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15-11x } & = & -3 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & -13x \color{blue}{-11x } & = & -3 \color{blue}{-15} \\\Leftrightarrow &-24x & = &-18\\\Leftrightarrow & \color{red}{-24}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-24}x}{ \color{blue}{ -24}} & = & \frac{-18}{-24} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+1}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1-x } & = & -8 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -8 \color{blue}{-1} \\\Leftrightarrow &7x & = &-9\\\Leftrightarrow & \color{red}{7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-15}& = & -15 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15-13x } & = & -15 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & 11x \color{blue}{-13x } & = & -15 \color{blue}{+15} \\\Leftrightarrow &-2x & = &0\\\Leftrightarrow & \color{red}{-2}x & = &0\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{0}{-2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+6}& = & -10 \color{red}{ +6x } \\\Leftrightarrow & 11x \color{red}{+6}\color{blue}{-6-6x } & = & -10 \color{red}{ +6x }\color{blue}{-6-6x } \\\Leftrightarrow & 11x \color{blue}{-6x } & = & -10 \color{blue}{-6} \\\Leftrightarrow &5x & = &-16\\\Leftrightarrow & \color{red}{5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-16}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+6}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+6}\color{blue}{-6+2x } & = & 2 \color{red}{ -2x }\color{blue}{-6+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 2 \color{blue}{-6} \\\Leftrightarrow &13x & = &-4\\\Leftrightarrow & \color{red}{13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-11}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-x } & = & -11 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -11 \color{blue}{+11} \\\Leftrightarrow &-15x & = &0\\\Leftrightarrow & \color{red}{-15}x & = &0\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{0}{-15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-11}& = & 2 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11-2x } & = & 2 \color{red}{ +2x }\color{blue}{+11-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & 2 \color{blue}{+11} \\\Leftrightarrow &-3x & = &13\\\Leftrightarrow & \color{red}{-3}x & = &13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)