Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+11}& = & -10 \color{red}{ +14x } \\\Leftrightarrow & 9x \color{red}{+11}\color{blue}{-11-14x } & = & -10 \color{red}{ +14x }\color{blue}{-11-14x } \\\Leftrightarrow & 9x \color{blue}{-14x } & = & -10 \color{blue}{-11} \\\Leftrightarrow &-5x & = &-21\\\Leftrightarrow & \color{red}{-5}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-21}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{21}{5} } & & \\ & V = \left\{ \frac{21}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+14}& = & 4 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14-12x } & = & 4 \color{red}{ +12x }\color{blue}{-14-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &-x & = &-10\\\Leftrightarrow & \color{red}{-}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-10}{-1} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+4}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4-x } & = & 13 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 13 \color{blue}{-4} \\\Leftrightarrow &5x & = &9\\\Leftrightarrow & \color{red}{5}x & = &9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-4}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-4}\color{blue}{+4-13x } & = & 1 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 1 \color{blue}{+4} \\\Leftrightarrow &-25x & = &5\\\Leftrightarrow & \color{red}{-25}x & = &5\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{5}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+11}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-7x } & = & -1 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &-20x & = &-12\\\Leftrightarrow & \color{red}{-20}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-12}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-8}& = & 5 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8-5x } & = & 5 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 5 \color{blue}{+8} \\\Leftrightarrow &-9x & = &13\\\Leftrightarrow & \color{red}{-9}x & = &13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+3}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-9x } & = & -13 \color{red}{ +9x }\color{blue}{-3-9x } \\\Leftrightarrow & -13x \color{blue}{-9x } & = & -13 \color{blue}{-3} \\\Leftrightarrow &-22x & = &-16\\\Leftrightarrow & \color{red}{-22}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-22}x}{ \color{blue}{ -22}} & = & \frac{-16}{-22} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-12}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-12}\color{blue}{+12-x } & = & 8 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 8 \color{blue}{+12} \\\Leftrightarrow &-15x & = &20\\\Leftrightarrow & \color{red}{-15}x & = &20\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{20}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-3}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3-x } & = & 5 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 5 \color{blue}{+3} \\\Leftrightarrow &-7x & = &8\\\Leftrightarrow & \color{red}{-7}x & = &8\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{8}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+12}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12-x } & = & 4 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 4 \color{blue}{-12} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-5}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-x } & = & 11 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 11 \color{blue}{+5} \\\Leftrightarrow &x & = &16\\\Leftrightarrow & \color{red}{}x & = &16\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 16 \\\Leftrightarrow & \color{green}{ x = 16 } & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{+2}& = & -12 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2-4x } & = & -12 \color{red}{ +4x }\color{blue}{-2-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -12 \color{blue}{-2} \\\Leftrightarrow &-19x & = &-14\\\Leftrightarrow & \color{red}{-19}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-14}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{14}{19} } & & \\ & V = \left\{ \frac{14}{19} \right\} & \\\end{align}\)