Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-9}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-x } & = & 4 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 4 \color{blue}{+9} \\\Leftrightarrow &-6x & = &13\\\Leftrightarrow & \color{red}{-6}x & = &13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-5}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5+11x } & = & 2 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 2 \color{blue}{+5} \\\Leftrightarrow &17x & = &7\\\Leftrightarrow & \color{red}{17}x & = &7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-10}& = & -2 \color{red}{ -2x } \\\Leftrightarrow & -x \color{red}{-10}\color{blue}{+10+2x } & = & -2 \color{red}{ -2x }\color{blue}{+10+2x } \\\Leftrightarrow & -x \color{blue}{+2x } & = & -2 \color{blue}{+10} \\\Leftrightarrow &x & = &8\\\Leftrightarrow & \color{red}{}x & = &8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 8 \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+8}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+8}\color{blue}{-8-x } & = & -11 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -11 \color{blue}{-8} \\\Leftrightarrow &11x & = &-19\\\Leftrightarrow & \color{red}{11}x & = &-19\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-19}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{11} } & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+5}& = & -2 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5+7x } & = & -2 \color{red}{ -7x }\color{blue}{-5+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -2 \color{blue}{-5} \\\Leftrightarrow &15x & = &-7\\\Leftrightarrow & \color{red}{15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-13}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13-11x } & = & -6 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -6 \color{blue}{+13} \\\Leftrightarrow &x & = &7\\\Leftrightarrow & \color{red}{}x & = &7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 7 \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-6}& = & -14 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-6}\color{blue}{+6+10x } & = & -14 \color{red}{ -10x }\color{blue}{+6+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & -14 \color{blue}{+6} \\\Leftrightarrow &21x & = &-8\\\Leftrightarrow & \color{red}{21}x & = &-8\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-8}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{21} } & & \\ & V = \left\{ \frac{-8}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+2}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+2}\color{blue}{-2-x } & = & 3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 3 \color{blue}{-2} \\\Leftrightarrow &-8x & = &1\\\Leftrightarrow & \color{red}{-8}x & = &1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-12}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-13x } & = & -5 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -5 \color{blue}{+12} \\\Leftrightarrow &-19x & = &7\\\Leftrightarrow & \color{red}{-19}x & = &7\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{7}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{19} } & & \\ & V = \left\{ \frac{-7}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{+4}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+4}\color{blue}{-4-x } & = & -2 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &-12x & = &-6\\\Leftrightarrow & \color{red}{-12}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+10}& = & -2 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10+8x } & = & -2 \color{red}{ -8x }\color{blue}{-10+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & -2 \color{blue}{-10} \\\Leftrightarrow &19x & = &-12\\\Leftrightarrow & \color{red}{19}x & = &-12\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-12}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{19} } & & \\ & V = \left\{ \frac{-12}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-5}& = & 15 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5+9x } & = & 15 \color{red}{ -9x }\color{blue}{+5+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & 15 \color{blue}{+5} \\\Leftrightarrow &8x & = &20\\\Leftrightarrow & \color{red}{8}x & = &20\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{20}{8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)