Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-10}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-10}\color{blue}{+10-x } & = & 14 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 14 \color{blue}{+10} \\\Leftrightarrow &-10x & = &24\\\Leftrightarrow & \color{red}{-10}x & = &24\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{24}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+7}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-x } & = & 12 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 12 \color{blue}{-7} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{-9}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9-x } & = & -1 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -1 \color{blue}{+9} \\\Leftrightarrow &-15x & = &8\\\Leftrightarrow & \color{red}{-15}x & = &8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+3}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-13x } & = & 11 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 11 \color{blue}{-3} \\\Leftrightarrow &-19x & = &8\\\Leftrightarrow & \color{red}{-19}x & = &8\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{8}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{19} } & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+1}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+1}\color{blue}{-1-x } & = & -9 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -9 \color{blue}{-1} \\\Leftrightarrow &-3x & = &-10\\\Leftrightarrow & \color{red}{-3}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+7}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+7}\color{blue}{-7-x } & = & 9 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 9 \color{blue}{-7} \\\Leftrightarrow &-13x & = &2\\\Leftrightarrow & \color{red}{-13}x & = &2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-4}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{-4}\color{blue}{+4-11x } & = & 9 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & 9 \color{blue}{+4} \\\Leftrightarrow &-13x & = &13\\\Leftrightarrow & \color{red}{-13}x & = &13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{13}{-13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-10}& = & -6 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10-6x } & = & -6 \color{red}{ +6x }\color{blue}{+10-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & -6 \color{blue}{+10} \\\Leftrightarrow &-17x & = &4\\\Leftrightarrow & \color{red}{-17}x & = &4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-9}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-x } & = & 6 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &-3x & = &15\\\Leftrightarrow & \color{red}{-3}x & = &15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{15}{-3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+13}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{+13}\color{blue}{-13-11x } & = & -8 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & -8 \color{blue}{-13} \\\Leftrightarrow &-x & = &-21\\\Leftrightarrow & \color{red}{-}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-21}{-1} \\\Leftrightarrow & \color{green}{ x = 21 } & & \\ & V = \left\{ 21 \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+13}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+13}\color{blue}{-13-x } & = & -9 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -9 \color{blue}{-13} \\\Leftrightarrow &-15x & = &-22\\\Leftrightarrow & \color{red}{-15}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-22}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{22}{15} } & & \\ & V = \left\{ \frac{22}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-12}& = & -15 \color{red}{ -4x } \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12+4x } & = & -15 \color{red}{ -4x }\color{blue}{+12+4x } \\\Leftrightarrow & x \color{blue}{+4x } & = & -15 \color{blue}{+12} \\\Leftrightarrow &5x & = &-3\\\Leftrightarrow & \color{red}{5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)