Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+8}& = & -12 \color{red}{ -14x } \\\Leftrightarrow & x \color{red}{+8}\color{blue}{-8+14x } & = & -12 \color{red}{ -14x }\color{blue}{-8+14x } \\\Leftrightarrow & x \color{blue}{+14x } & = & -12 \color{blue}{-8} \\\Leftrightarrow &15x & = &-20\\\Leftrightarrow & \color{red}{15}x & = &-20\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-20}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+4}& = & -1 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4+9x } & = & -1 \color{red}{ -9x }\color{blue}{-4+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & -1 \color{blue}{-4} \\\Leftrightarrow &8x & = &-5\\\Leftrightarrow & \color{red}{8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-5}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+12}& = & -12 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+12}\color{blue}{-12-6x } & = & -12 \color{red}{ +6x }\color{blue}{-12-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -12 \color{blue}{-12} \\\Leftrightarrow &-11x & = &-24\\\Leftrightarrow & \color{red}{-11}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-24}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{24}{11} } & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+3}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-x } & = & 10 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 10 \color{blue}{-3} \\\Leftrightarrow &-4x & = &7\\\Leftrightarrow & \color{red}{-4}x & = &7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+13}& = & -5 \color{red}{ +12x } \\\Leftrightarrow & -7x \color{red}{+13}\color{blue}{-13-12x } & = & -5 \color{red}{ +12x }\color{blue}{-13-12x } \\\Leftrightarrow & -7x \color{blue}{-12x } & = & -5 \color{blue}{-13} \\\Leftrightarrow &-19x & = &-18\\\Leftrightarrow & \color{red}{-19}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-18}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{18}{19} } & & \\ & V = \left\{ \frac{18}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+15}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15-7x } & = & 3 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & 13x \color{blue}{-7x } & = & 3 \color{blue}{-15} \\\Leftrightarrow &6x & = &-12\\\Leftrightarrow & \color{red}{6}x & = &-12\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-12}{6} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-3}& = & -11 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3+11x } & = & -11 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & -11 \color{blue}{+3} \\\Leftrightarrow &20x & = &-8\\\Leftrightarrow & \color{red}{20}x & = &-8\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-8}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+12}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12-5x } & = & 11 \color{red}{ +5x }\color{blue}{-12-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &7x & = &-1\\\Leftrightarrow & \color{red}{7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-5}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-5}\color{blue}{+5-5x } & = & -7 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -7 \color{blue}{+5} \\\Leftrightarrow &7x & = &-2\\\Leftrightarrow & \color{red}{7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-5}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-x } & = & -8 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -8 \color{blue}{+5} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-4}& = & 1 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4+2x } & = & 1 \color{red}{ -2x }\color{blue}{+4+2x } \\\Leftrightarrow & x \color{blue}{+2x } & = & 1 \color{blue}{+4} \\\Leftrightarrow &3x & = &5\\\Leftrightarrow & \color{red}{3}x & = &5\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{5}{3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+9}& = & 15 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9+7x } & = & 15 \color{red}{ -7x }\color{blue}{-9+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 15 \color{blue}{-9} \\\Leftrightarrow &11x & = &6\\\Leftrightarrow & \color{red}{11}x & = &6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)