Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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