Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+4}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4-x } & = & 13 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 13 \color{blue}{-4} \\\Leftrightarrow &-15x & = &9\\\Leftrightarrow & \color{red}{-15}x & = &9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-14}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-14}\color{blue}{+14-x } & = & 8 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 8 \color{blue}{+14} \\\Leftrightarrow &-13x & = &22\\\Leftrightarrow & \color{red}{-13}x & = &22\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{22}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{13} } & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{-9}& = & -6 \color{red}{ +8x } \\\Leftrightarrow & 13x \color{red}{-9}\color{blue}{+9-8x } & = & -6 \color{red}{ +8x }\color{blue}{+9-8x } \\\Leftrightarrow & 13x \color{blue}{-8x } & = & -6 \color{blue}{+9} \\\Leftrightarrow &5x & = &3\\\Leftrightarrow & \color{red}{5}x & = &3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-1}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-x } & = & 10 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 10 \color{blue}{+1} \\\Leftrightarrow &-13x & = &11\\\Leftrightarrow & \color{red}{-13}x & = &11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+5}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5-x } & = & -12 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -12 \color{blue}{-5} \\\Leftrightarrow &13x & = &-17\\\Leftrightarrow & \color{red}{13}x & = &-17\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-17}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+5}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+5}\color{blue}{-5-x } & = & -13 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -13 \color{blue}{-5} \\\Leftrightarrow &-13x & = &-18\\\Leftrightarrow & \color{red}{-13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-18}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-3}& = & -7 \color{red}{ +14x } \\\Leftrightarrow & -x \color{red}{-3}\color{blue}{+3-14x } & = & -7 \color{red}{ +14x }\color{blue}{+3-14x } \\\Leftrightarrow & -x \color{blue}{-14x } & = & -7 \color{blue}{+3} \\\Leftrightarrow &-15x & = &-4\\\Leftrightarrow & \color{red}{-15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-3}& = & 2 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3+10x } & = & 2 \color{red}{ -10x }\color{blue}{+3+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 2 \color{blue}{+3} \\\Leftrightarrow &21x & = &5\\\Leftrightarrow & \color{red}{21}x & = &5\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{5}{21} \\\Leftrightarrow & \color{green}{ x = \frac{5}{21} } & & \\ & V = \left\{ \frac{5}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-6}& = & -15 \color{red}{ +13x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6-13x } & = & -15 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & 5x \color{blue}{-13x } & = & -15 \color{blue}{+6} \\\Leftrightarrow &-8x & = &-9\\\Leftrightarrow & \color{red}{-8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+9}& = & 9 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9-5x } & = & 9 \color{red}{ +5x }\color{blue}{-9-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+5}& = & 4 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5-4x } & = & 4 \color{red}{ +4x }\color{blue}{-5-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &-19x & = &-1\\\Leftrightarrow & \color{red}{-19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-4}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-4}\color{blue}{+4-x } & = & 12 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 12 \color{blue}{+4} \\\Leftrightarrow &-8x & = &16\\\Leftrightarrow & \color{red}{-8}x & = &16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{16}{-8} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)