Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{-15}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-15}\color{blue}{+15-x } & = & -5 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -5 \color{blue}{+15} \\\Leftrightarrow &-9x & = &10\\\Leftrightarrow & \color{red}{-9}x & = &10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+4}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4-x } & = & 9 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 9 \color{blue}{-4} \\\Leftrightarrow &-7x & = &5\\\Leftrightarrow & \color{red}{-7}x & = &5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{-7}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7-13x } & = & 11 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & 11 \color{blue}{+7} \\\Leftrightarrow &-3x & = &18\\\Leftrightarrow & \color{red}{-3}x & = &18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{18}{-3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+13}& = & 4 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13-4x } & = & 4 \color{red}{ +4x }\color{blue}{-13-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & 4 \color{blue}{-13} \\\Leftrightarrow &11x & = &-9\\\Leftrightarrow & \color{red}{11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-15}& = & 1 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15-3x } & = & 1 \color{red}{ +3x }\color{blue}{+15-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & 1 \color{blue}{+15} \\\Leftrightarrow &-5x & = &16\\\Leftrightarrow & \color{red}{-5}x & = &16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-13}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-13}\color{blue}{+13-x } & = & 3 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 3 \color{blue}{+13} \\\Leftrightarrow &-16x & = &16\\\Leftrightarrow & \color{red}{-16}x & = &16\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{16}{-16} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{+3}& = & 6 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3-5x } & = & 6 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 6 \color{blue}{-3} \\\Leftrightarrow &-17x & = &3\\\Leftrightarrow & \color{red}{-17}x & = &3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+5}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5-5x } & = & 7 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 7 \color{blue}{-5} \\\Leftrightarrow &-14x & = &2\\\Leftrightarrow & \color{red}{-14}x & = &2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+14}& = & 11 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14-14x } & = & 11 \color{red}{ +14x }\color{blue}{-14-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & 11 \color{blue}{-14} \\\Leftrightarrow &-x & = &-3\\\Leftrightarrow & \color{red}{-}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-3}{-1} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-5}& = & 14 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5+5x } & = & 14 \color{red}{ -5x }\color{blue}{+5+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &11x & = &19\\\Leftrightarrow & \color{red}{11}x & = &19\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{19}{11} \\\Leftrightarrow & \color{green}{ x = \frac{19}{11} } & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+6}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+6}\color{blue}{-6-x } & = & -6 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -6 \color{blue}{-6} \\\Leftrightarrow &-7x & = &-12\\\Leftrightarrow & \color{red}{-7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+13}& = & -13 \color{red}{ +5x } \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13-5x } & = & -13 \color{red}{ +5x }\color{blue}{-13-5x } \\\Leftrightarrow & x \color{blue}{-5x } & = & -13 \color{blue}{-13} \\\Leftrightarrow &-4x & = &-26\\\Leftrightarrow & \color{red}{-4}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-26}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{2} } & & \\ & V = \left\{ \frac{13}{2} \right\} & \\\end{align}\)