Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+13}& = & 6 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13+5x } & = & 6 \color{red}{ -5x }\color{blue}{-13+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 6 \color{blue}{-13} \\\Leftrightarrow &11x & = &-7\\\Leftrightarrow & \color{red}{11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-6}& = & -5 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{-6}\color{blue}{+6+7x } & = & -5 \color{red}{ -7x }\color{blue}{+6+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & -5 \color{blue}{+6} \\\Leftrightarrow &18x & = &1\\\Leftrightarrow & \color{red}{18}x & = &1\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{1}{18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{18} } & & \\ & V = \left\{ \frac{1}{18} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+12}& = & -7 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12+15x } & = & -7 \color{red}{ -15x }\color{blue}{-12+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & -7 \color{blue}{-12} \\\Leftrightarrow &23x & = &-19\\\Leftrightarrow & \color{red}{23}x & = &-19\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-19}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{23} } & & \\ & V = \left\{ \frac{-19}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{+15}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+15}\color{blue}{-15-x } & = & -15 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -15 \color{blue}{-15} \\\Leftrightarrow &-15x & = &-30\\\Leftrightarrow & \color{red}{-15}x & = &-30\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-30}{-15} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{-14}& = & 6 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-14}\color{blue}{+14+6x } & = & 6 \color{red}{ -6x }\color{blue}{+14+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & 6 \color{blue}{+14} \\\Leftrightarrow &13x & = &20\\\Leftrightarrow & \color{red}{13}x & = &20\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{20}{13} \\\Leftrightarrow & \color{green}{ x = \frac{20}{13} } & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{+15}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15-x } & = & -6 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -6 \color{blue}{-15} \\\Leftrightarrow &-8x & = &-21\\\Leftrightarrow & \color{red}{-8}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-21}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{21}{8} } & & \\ & V = \left\{ \frac{21}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+7}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7-x } & = & -7 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -7 \color{blue}{-7} \\\Leftrightarrow &-15x & = &-14\\\Leftrightarrow & \color{red}{-15}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{14}{15} } & & \\ & V = \left\{ \frac{14}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+4}& = & -13 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-11x } & = & -13 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -13 \color{blue}{-4} \\\Leftrightarrow &-21x & = &-17\\\Leftrightarrow & \color{red}{-21}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-17}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{17}{21} } & & \\ & V = \left\{ \frac{17}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-1}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-5x } & = & 10 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & 10 \color{blue}{+1} \\\Leftrightarrow &-19x & = &11\\\Leftrightarrow & \color{red}{-19}x & = &11\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{11}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{19} } & & \\ & V = \left\{ \frac{-11}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+8}& = & -5 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8-5x } & = & -5 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -5 \color{blue}{-8} \\\Leftrightarrow &-9x & = &-13\\\Leftrightarrow & \color{red}{-9}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+15}& = & -6 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15+8x } & = & -6 \color{red}{ -8x }\color{blue}{-15+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & -6 \color{blue}{-15} \\\Leftrightarrow &19x & = &-21\\\Leftrightarrow & \color{red}{19}x & = &-21\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-21}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{19} } & & \\ & V = \left\{ \frac{-21}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{-13}& = & -12 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13-10x } & = & -12 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & -12 \color{blue}{+13} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)