Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-13}& = & 11 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13-14x } & = & 11 \color{red}{ +14x }\color{blue}{+13-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 11 \color{blue}{+13} \\\Leftrightarrow &-27x & = &24\\\Leftrightarrow & \color{red}{-27}x & = &24\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{24}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-1}& = & 9 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1+8x } & = & 9 \color{red}{ -8x }\color{blue}{+1+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &11x & = &10\\\Leftrightarrow & \color{red}{11}x & = &10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-12}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12-x } & = & -4 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -4 \color{blue}{+12} \\\Leftrightarrow &-10x & = &8\\\Leftrightarrow & \color{red}{-10}x & = &8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-7}& = & 10 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7-6x } & = & 10 \color{red}{ +6x }\color{blue}{+7-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & 10 \color{blue}{+7} \\\Leftrightarrow &-x & = &17\\\Leftrightarrow & \color{red}{-}x & = &17\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{17}{-1} \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+9}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9-7x } & = & -3 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & -3 \color{blue}{-9} \\\Leftrightarrow &5x & = &-12\\\Leftrightarrow & \color{red}{5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+12}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12-x } & = & 14 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 14 \color{blue}{-12} \\\Leftrightarrow &-15x & = &2\\\Leftrightarrow & \color{red}{-15}x & = &2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+6}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+6}\color{blue}{-6-13x } & = & 6 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 6 \color{blue}{-6} \\\Leftrightarrow &-19x & = &0\\\Leftrightarrow & \color{red}{-19}x & = &0\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{0}{-19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+1}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-13x } & = & -4 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -4 \color{blue}{-1} \\\Leftrightarrow &-25x & = &-5\\\Leftrightarrow & \color{red}{-25}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-5}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{+15}& = & -9 \color{red}{ +12x } \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15-12x } & = & -9 \color{red}{ +12x }\color{blue}{-15-12x } \\\Leftrightarrow & -7x \color{blue}{-12x } & = & -9 \color{blue}{-15} \\\Leftrightarrow &-19x & = &-24\\\Leftrightarrow & \color{red}{-19}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-24}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{24}{19} } & & \\ & V = \left\{ \frac{24}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+3}& = & -2 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3+3x } & = & -2 \color{red}{ -3x }\color{blue}{-3+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -2 \color{blue}{-3} \\\Leftrightarrow &13x & = &-5\\\Leftrightarrow & \color{red}{13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{+2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+2}\color{blue}{-2-x } & = & 4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-13}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13-x } & = & -1 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -1 \color{blue}{+13} \\\Leftrightarrow &-5x & = &12\\\Leftrightarrow & \color{red}{-5}x & = &12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)