Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-11}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11-x } & = & 11 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 11 \color{blue}{+11} \\\Leftrightarrow &-11x & = &22\\\Leftrightarrow & \color{red}{-11}x & = &22\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{22}{-11} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-13}& = & 15 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-13}\color{blue}{+13+14x } & = & 15 \color{red}{ -14x }\color{blue}{+13+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 15 \color{blue}{+13} \\\Leftrightarrow &29x & = &28\\\Leftrightarrow & \color{red}{29}x & = &28\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{28}{29} \\\Leftrightarrow & \color{green}{ x = \frac{28}{29} } & & \\ & V = \left\{ \frac{28}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+1}& = & -12 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1+11x } & = & -12 \color{red}{ -11x }\color{blue}{-1+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -12 \color{blue}{-1} \\\Leftrightarrow &23x & = &-13\\\Leftrightarrow & \color{red}{23}x & = &-13\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-13}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{23} } & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-10}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10-x } & = & -12 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -12 \color{blue}{+10} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+6}& = & 11 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6-6x } & = & 11 \color{red}{ +6x }\color{blue}{-6-6x } \\\Leftrightarrow & x \color{blue}{-6x } & = & 11 \color{blue}{-6} \\\Leftrightarrow &-5x & = &5\\\Leftrightarrow & \color{red}{-5}x & = &5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{5}{-5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+5}& = & 11 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5+15x } & = & 11 \color{red}{ -15x }\color{blue}{-5+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 11 \color{blue}{-5} \\\Leftrightarrow &19x & = &6\\\Leftrightarrow & \color{red}{19}x & = &6\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{6}{19} \\\Leftrightarrow & \color{green}{ x = \frac{6}{19} } & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+13}& = & 14 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13+4x } & = & 14 \color{red}{ -4x }\color{blue}{-13+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 14 \color{blue}{-13} \\\Leftrightarrow &13x & = &1\\\Leftrightarrow & \color{red}{13}x & = &1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-1}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-11x } & = & 12 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 12 \color{blue}{+1} \\\Leftrightarrow &-21x & = &13\\\Leftrightarrow & \color{red}{-21}x & = &13\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{13}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{21} } & & \\ & V = \left\{ \frac{-13}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-13}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13-13x } & = & 14 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & 14 \color{blue}{+13} \\\Leftrightarrow &-3x & = &27\\\Leftrightarrow & \color{red}{-3}x & = &27\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{27}{-3} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{+5}& = & 15 \color{red}{ +14x } \\\Leftrightarrow & x \color{red}{+5}\color{blue}{-5-14x } & = & 15 \color{red}{ +14x }\color{blue}{-5-14x } \\\Leftrightarrow & x \color{blue}{-14x } & = & 15 \color{blue}{-5} \\\Leftrightarrow &-13x & = &10\\\Leftrightarrow & \color{red}{-13}x & = &10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+14}& = & -15 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14-4x } & = & -15 \color{red}{ +4x }\color{blue}{-14-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & -15 \color{blue}{-14} \\\Leftrightarrow &-x & = &-29\\\Leftrightarrow & \color{red}{-}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-29}{-1} \\\Leftrightarrow & \color{green}{ x = 29 } & & \\ & V = \left\{ 29 \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{+10}& = & -12 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{+10}\color{blue}{-10-10x } & = & -12 \color{red}{ +10x }\color{blue}{-10-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & -12 \color{blue}{-10} \\\Leftrightarrow &-7x & = &-22\\\Leftrightarrow & \color{red}{-7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-22}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{22}{7} } & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)