Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-5}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-x } & = & -7 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -7 \color{blue}{+5} \\\Leftrightarrow &x & = &-2\\\Leftrightarrow & \color{red}{}x & = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-4}& = & 1 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-4}\color{blue}{+4+7x } & = & 1 \color{red}{ -7x }\color{blue}{+4+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 1 \color{blue}{+4} \\\Leftrightarrow &19x & = &5\\\Leftrightarrow & \color{red}{19}x & = &5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-15}& = & 12 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-15}\color{blue}{+15+14x } & = & 12 \color{red}{ -14x }\color{blue}{+15+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 12 \color{blue}{+15} \\\Leftrightarrow &29x & = &27\\\Leftrightarrow & \color{red}{29}x & = &27\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{27}{29} \\\Leftrightarrow & \color{green}{ x = \frac{27}{29} } & & \\ & V = \left\{ \frac{27}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-1}& = & -13 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1+4x } & = & -13 \color{red}{ -4x }\color{blue}{+1+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -13 \color{blue}{+1} \\\Leftrightarrow &13x & = &-12\\\Leftrightarrow & \color{red}{13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+13}& = & 7 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13-4x } & = & 7 \color{red}{ +4x }\color{blue}{-13-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & 7 \color{blue}{-13} \\\Leftrightarrow &5x & = &-6\\\Leftrightarrow & \color{red}{5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+11}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+11}\color{blue}{-11-x } & = & 9 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 9 \color{blue}{-11} \\\Leftrightarrow &-15x & = &-2\\\Leftrightarrow & \color{red}{-15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-13}& = & 11 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13+10x } & = & 11 \color{red}{ -10x }\color{blue}{+13+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 11 \color{blue}{+13} \\\Leftrightarrow &21x & = &24\\\Leftrightarrow & \color{red}{21}x & = &24\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{24}{21} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-2}\color{blue}{+2-x } & = & -10 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -10 \color{blue}{+2} \\\Leftrightarrow &-5x & = &-8\\\Leftrightarrow & \color{red}{-5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+3}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+3}\color{blue}{-3-5x } & = & 14 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 14 \color{blue}{-3} \\\Leftrightarrow &7x & = &11\\\Leftrightarrow & \color{red}{7}x & = &11\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{11}{7} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+4}& = & -3 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-4x } & = & -3 \color{red}{ +4x }\color{blue}{-4-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &-11x & = &-7\\\Leftrightarrow & \color{red}{-11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+9}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+9}\color{blue}{-9-13x } & = & 6 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 6 \color{blue}{-9} \\\Leftrightarrow &-19x & = &-3\\\Leftrightarrow & \color{red}{-19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+13}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+13}\color{blue}{-13-5x } & = & 15 \color{red}{ +5x }\color{blue}{-13-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)