Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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