Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{-1}& = & 13 \color{red}{ -14x } \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1+14x } & = & 13 \color{red}{ -14x }\color{blue}{+1+14x } \\\Leftrightarrow & x \color{blue}{+14x } & = & 13 \color{blue}{+1} \\\Leftrightarrow &15x & = &14\\\Leftrightarrow & \color{red}{15}x & = &14\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{14}{15} \\\Leftrightarrow & \color{green}{ x = \frac{14}{15} } & & \\ & V = \left\{ \frac{14}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{-8}& = & 12 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8+9x } & = & 12 \color{red}{ -9x }\color{blue}{+8+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 12 \color{blue}{+8} \\\Leftrightarrow &19x & = &20\\\Leftrightarrow & \color{red}{19}x & = &20\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{20}{19} \\\Leftrightarrow & \color{green}{ x = \frac{20}{19} } & & \\ & V = \left\{ \frac{20}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+5}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5-x } & = & 7 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 7 \color{blue}{-5} \\\Leftrightarrow &12x & = &2\\\Leftrightarrow & \color{red}{12}x & = &2\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{2}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-13}& = & -13 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13+5x } & = & -13 \color{red}{ -5x }\color{blue}{+13+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -13 \color{blue}{+13} \\\Leftrightarrow &8x & = &0\\\Leftrightarrow & \color{red}{8}x & = &0\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{0}{8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+11}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+11}\color{blue}{-11-x } & = & 14 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 14 \color{blue}{-11} \\\Leftrightarrow &5x & = &3\\\Leftrightarrow & \color{red}{5}x & = &3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-2}& = & 15 \color{red}{ -9x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2+9x } & = & 15 \color{red}{ -9x }\color{blue}{+2+9x } \\\Leftrightarrow & 7x \color{blue}{+9x } & = & 15 \color{blue}{+2} \\\Leftrightarrow &16x & = &17\\\Leftrightarrow & \color{red}{16}x & = &17\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{17}{16} \\\Leftrightarrow & \color{green}{ x = \frac{17}{16} } & & \\ & V = \left\{ \frac{17}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{+12}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12-x } & = & -6 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -6 \color{blue}{-12} \\\Leftrightarrow &-12x & = &-18\\\Leftrightarrow & \color{red}{-12}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-18}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-13}& = & -2 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-9x } & = & -2 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & -2 \color{blue}{+13} \\\Leftrightarrow &-20x & = &11\\\Leftrightarrow & \color{red}{-20}x & = &11\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{11}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{20} } & & \\ & V = \left\{ \frac{-11}{20} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{+12}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+12}\color{blue}{-12-x } & = & -3 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -3 \color{blue}{-12} \\\Leftrightarrow &-8x & = &-15\\\Leftrightarrow & \color{red}{-8}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-15}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{15}{8} } & & \\ & V = \left\{ \frac{15}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-6}& = & -6 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6+15x } & = & -6 \color{red}{ -15x }\color{blue}{+6+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -6 \color{blue}{+6} \\\Leftrightarrow &19x & = &0\\\Leftrightarrow & \color{red}{19}x & = &0\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{0}{19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-12}& = & 5 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-12}\color{blue}{+12-6x } & = & 5 \color{red}{ +6x }\color{blue}{+12-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 5 \color{blue}{+12} \\\Leftrightarrow &-17x & = &17\\\Leftrightarrow & \color{red}{-17}x & = &17\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{17}{-17} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+2}& = & 1 \color{red}{ +9x } \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2-9x } & = & 1 \color{red}{ +9x }\color{blue}{-2-9x } \\\Leftrightarrow & -x \color{blue}{-9x } & = & 1 \color{blue}{-2} \\\Leftrightarrow &-10x & = &-1\\\Leftrightarrow & \color{red}{-10}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)