Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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