Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+12}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+12}\color{blue}{-12-x } & = & 14 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 14 \color{blue}{-12} \\\Leftrightarrow &-16x & = &2\\\Leftrightarrow & \color{red}{-16}x & = &2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+13}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+13}\color{blue}{-13-x } & = & -4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -4 \color{blue}{-13} \\\Leftrightarrow &-4x & = &-17\\\Leftrightarrow & \color{red}{-4}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-17}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{17}{4} } & & \\ & V = \left\{ \frac{17}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+14}& = & -1 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14-3x } & = & -1 \color{red}{ +3x }\color{blue}{-14-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-15\\\Leftrightarrow & \color{red}{-5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-15}{-5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-2}& = & 3 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2+8x } & = & 3 \color{red}{ -8x }\color{blue}{+2+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 3 \color{blue}{+2} \\\Leftrightarrow &19x & = &5\\\Leftrightarrow & \color{red}{19}x & = &5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-12}& = & -3 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12+5x } & = & -3 \color{red}{ -5x }\color{blue}{+12+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -3 \color{blue}{+12} \\\Leftrightarrow &11x & = &9\\\Leftrightarrow & \color{red}{11}x & = &9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-6}& = & 12 \color{red}{ +8x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6-8x } & = & 12 \color{red}{ +8x }\color{blue}{+6-8x } \\\Leftrightarrow & x \color{blue}{-8x } & = & 12 \color{blue}{+6} \\\Leftrightarrow &-7x & = &18\\\Leftrightarrow & \color{red}{-7}x & = &18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+1}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+1}\color{blue}{-1-x } & = & -11 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -11 \color{blue}{-1} \\\Leftrightarrow &-14x & = &-12\\\Leftrightarrow & \color{red}{-14}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-14}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14-7x } & = & 2 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 2 \color{blue}{+14} \\\Leftrightarrow &-20x & = &16\\\Leftrightarrow & \color{red}{-20}x & = &16\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{16}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+7}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7+11x } & = & 7 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 7 \color{blue}{-7} \\\Leftrightarrow &23x & = &0\\\Leftrightarrow & \color{red}{23}x & = &0\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{0}{23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+8}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8-x } & = & 10 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 10 \color{blue}{-8} \\\Leftrightarrow &-15x & = &2\\\Leftrightarrow & \color{red}{-15}x & = &2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-4}& = & 8 \color{red}{ -8x } \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4+8x } & = & 8 \color{red}{ -8x }\color{blue}{+4+8x } \\\Leftrightarrow & x \color{blue}{+8x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &9x & = &12\\\Leftrightarrow & \color{red}{9}x & = &12\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{12}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+13}& = & -11 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13+8x } & = & -11 \color{red}{ -8x }\color{blue}{-13+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -11 \color{blue}{-13} \\\Leftrightarrow &17x & = &-24\\\Leftrightarrow & \color{red}{17}x & = &-24\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-24}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{17} } & & \\ & V = \left\{ \frac{-24}{17} \right\} & \\\end{align}\)