Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-10}& = & 14 \color{red}{ +15x } \\\Leftrightarrow & -x \color{red}{-10}\color{blue}{+10-15x } & = & 14 \color{red}{ +15x }\color{blue}{+10-15x } \\\Leftrightarrow & -x \color{blue}{-15x } & = & 14 \color{blue}{+10} \\\Leftrightarrow &-16x & = &24\\\Leftrightarrow & \color{red}{-16}x & = &24\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{24}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+6}& = & 14 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6+3x } & = & 14 \color{red}{ -3x }\color{blue}{-6+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 14 \color{blue}{-6} \\\Leftrightarrow &10x & = &8\\\Leftrightarrow & \color{red}{10}x & = &8\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{8}{10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-6}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6-x } & = & -6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -6 \color{blue}{+6} \\\Leftrightarrow &-16x & = &0\\\Leftrightarrow & \color{red}{-16}x & = &0\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{0}{-16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{+6}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-x } & = & 14 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 14 \color{blue}{-6} \\\Leftrightarrow &-16x & = &8\\\Leftrightarrow & \color{red}{-16}x & = &8\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{8}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{-2}& = & 11 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2+9x } & = & 11 \color{red}{ -9x }\color{blue}{+2+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & 11 \color{blue}{+2} \\\Leftrightarrow &14x & = &13\\\Leftrightarrow & \color{red}{14}x & = &13\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{13}{14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{14} } & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-12}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12-11x } & = & 4 \color{red}{ +11x }\color{blue}{+12-11x } \\\Leftrightarrow & 9x \color{blue}{-11x } & = & 4 \color{blue}{+12} \\\Leftrightarrow &-2x & = &16\\\Leftrightarrow & \color{red}{-2}x & = &16\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{16}{-2} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+12}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12-x } & = & -15 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -15 \color{blue}{-12} \\\Leftrightarrow &x & = &-27\\\Leftrightarrow & \color{red}{}x & = &-27\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -27 \\\Leftrightarrow & \color{green}{ x = -27 } & & \\ & V = \left\{ -27 \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-2}& = & 5 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2-14x } & = & 5 \color{red}{ +14x }\color{blue}{+2-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & 5 \color{blue}{+2} \\\Leftrightarrow &-x & = &7\\\Leftrightarrow & \color{red}{-}x & = &7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{7}{-1} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{-3}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-x } & = & 7 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 7 \color{blue}{+3} \\\Leftrightarrow &-13x & = &10\\\Leftrightarrow & \color{red}{-13}x & = &10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-12}& = & 11 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12-8x } & = & 11 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & 11 \color{blue}{+12} \\\Leftrightarrow &-x & = &23\\\Leftrightarrow & \color{red}{-}x & = &23\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{23}{-1} \\\Leftrightarrow & \color{green}{ x = -23 } & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+15}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15-x } & = & -12 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -12 \color{blue}{-15} \\\Leftrightarrow &-12x & = &-27\\\Leftrightarrow & \color{red}{-12}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-27}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-2}\color{blue}{+2-x } & = & -10 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -10 \color{blue}{+2} \\\Leftrightarrow &-12x & = &-8\\\Leftrightarrow & \color{red}{-12}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)