Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+14}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-x } & = & -14 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -14 \color{blue}{-14} \\\Leftrightarrow &-14x & = &-28\\\Leftrightarrow & \color{red}{-14}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-28}{-14} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+14}& = & 9 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14+9x } & = & 9 \color{red}{ -9x }\color{blue}{-14+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 9 \color{blue}{-14} \\\Leftrightarrow &19x & = &-5\\\Leftrightarrow & \color{red}{19}x & = &-5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{19} } & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-11}& = & 4 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11-3x } & = & 4 \color{red}{ +3x }\color{blue}{+11-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & 4 \color{blue}{+11} \\\Leftrightarrow &5x & = &15\\\Leftrightarrow & \color{red}{5}x & = &15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{15}{5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-2}& = & 9 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{-2}\color{blue}{+2-12x } & = & 9 \color{red}{ +12x }\color{blue}{+2-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & 9 \color{blue}{+2} \\\Leftrightarrow &-11x & = &11\\\Leftrightarrow & \color{red}{-11}x & = &11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{11}{-11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-1}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1-x } & = & -2 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -2 \color{blue}{+1} \\\Leftrightarrow &-16x & = &-1\\\Leftrightarrow & \color{red}{-16}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{-14}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14-13x } & = & 15 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & 15 \color{blue}{+14} \\\Leftrightarrow &-9x & = &29\\\Leftrightarrow & \color{red}{-9}x & = &29\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{29}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{9} } & & \\ & V = \left\{ \frac{-29}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{+15}& = & -14 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15+11x } & = & -14 \color{red}{ -11x }\color{blue}{-15+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -14 \color{blue}{-15} \\\Leftrightarrow &17x & = &-29\\\Leftrightarrow & \color{red}{17}x & = &-29\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-29}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{17} } & & \\ & V = \left\{ \frac{-29}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+4}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4-5x } & = & -15 \color{red}{ +5x }\color{blue}{-4-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & -15 \color{blue}{-4} \\\Leftrightarrow &-7x & = &-19\\\Leftrightarrow & \color{red}{-7}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{19}{7} } & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+2}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-x } & = & -5 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -5 \color{blue}{-2} \\\Leftrightarrow &-9x & = &-7\\\Leftrightarrow & \color{red}{-9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5-x } & = & 13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &-13x & = &18\\\Leftrightarrow & \color{red}{-13}x & = &18\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{18}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{13} } & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+13}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13-x } & = & -15 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -15 \color{blue}{-13} \\\Leftrightarrow &5x & = &-28\\\Leftrightarrow & \color{red}{5}x & = &-28\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-28}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{5} } & & \\ & V = \left\{ \frac{-28}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7-x } & = & 14 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 14 \color{blue}{+7} \\\Leftrightarrow &-5x & = &21\\\Leftrightarrow & \color{red}{-5}x & = &21\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{21}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{5} } & & \\ & V = \left\{ \frac{-21}{5} \right\} & \\\end{align}\)