Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+15}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15-x } & = & -4 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -4 \color{blue}{-15} \\\Leftrightarrow &8x & = &-19\\\Leftrightarrow & \color{red}{8}x & = &-19\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-19}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{8} } & & \\ & V = \left\{ \frac{-19}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-12}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12-x } & = & 12 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &-10x & = &24\\\Leftrightarrow & \color{red}{-10}x & = &24\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{24}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{-6}& = & 8 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-6}\color{blue}{+6-6x } & = & 8 \color{red}{ +6x }\color{blue}{+6-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 8 \color{blue}{+6} \\\Leftrightarrow &-17x & = &14\\\Leftrightarrow & \color{red}{-17}x & = &14\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{14}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{17} } & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-15}& = & -11 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-12x } & = & -11 \color{red}{ +12x }\color{blue}{+15-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & -11 \color{blue}{+15} \\\Leftrightarrow &-23x & = &4\\\Leftrightarrow & \color{red}{-23}x & = &4\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{4}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{23} } & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{-5}& = & 7 \color{red}{ +4x } \\\Leftrightarrow & x \color{red}{-5}\color{blue}{+5-4x } & = & 7 \color{red}{ +4x }\color{blue}{+5-4x } \\\Leftrightarrow & x \color{blue}{-4x } & = & 7 \color{blue}{+5} \\\Leftrightarrow &-3x & = &12\\\Leftrightarrow & \color{red}{-3}x & = &12\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{12}{-3} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-7}& = & -15 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7-13x } & = & -15 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -15 \color{blue}{+7} \\\Leftrightarrow &-25x & = &-8\\\Leftrightarrow & \color{red}{-25}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-8}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{8}{25} } & & \\ & V = \left\{ \frac{8}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+2}\color{blue}{-2-x } & = & -10 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &-6x & = &-12\\\Leftrightarrow & \color{red}{-6}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-12}{-6} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-4}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4-11x } & = & 12 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 12 \color{blue}{+4} \\\Leftrightarrow &-5x & = &16\\\Leftrightarrow & \color{red}{-5}x & = &16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+2}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2-13x } & = & 7 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & 11x \color{blue}{-13x } & = & 7 \color{blue}{-2} \\\Leftrightarrow &-2x & = &5\\\Leftrightarrow & \color{red}{-2}x & = &5\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{5}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-4}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-4}\color{blue}{+4-x } & = & -15 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -15 \color{blue}{+4} \\\Leftrightarrow &-5x & = &-11\\\Leftrightarrow & \color{red}{-5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+6}& = & -14 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6+2x } & = & -14 \color{red}{ -2x }\color{blue}{-6+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & -14 \color{blue}{-6} \\\Leftrightarrow &11x & = &-20\\\Leftrightarrow & \color{red}{11}x & = &-20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+2}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-x } & = & 6 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 6 \color{blue}{-2} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)