Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{-15}& = & 14 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15-14x } & = & 14 \color{red}{ +14x }\color{blue}{+15-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & 14 \color{blue}{+15} \\\Leftrightarrow &-3x & = &29\\\Leftrightarrow & \color{red}{-3}x & = &29\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{29}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{3} } & & \\ & V = \left\{ \frac{-29}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-5}& = & -7 \color{red}{ +8x } \\\Leftrightarrow & 11x \color{red}{-5}\color{blue}{+5-8x } & = & -7 \color{red}{ +8x }\color{blue}{+5-8x } \\\Leftrightarrow & 11x \color{blue}{-8x } & = & -7 \color{blue}{+5} \\\Leftrightarrow &3x & = &-2\\\Leftrightarrow & \color{red}{3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-14}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14+11x } & = & -7 \color{red}{ -11x }\color{blue}{+14+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -7 \color{blue}{+14} \\\Leftrightarrow &17x & = &7\\\Leftrightarrow & \color{red}{17}x & = &7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+14}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14-11x } & = & 6 \color{red}{ +11x }\color{blue}{-14-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & 6 \color{blue}{-14} \\\Leftrightarrow &-16x & = &-8\\\Leftrightarrow & \color{red}{-16}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-8}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{-13}& = & -11 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13+4x } & = & -11 \color{red}{ -4x }\color{blue}{+13+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -11 \color{blue}{+13} \\\Leftrightarrow &9x & = &2\\\Leftrightarrow & \color{red}{9}x & = &2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-3}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3-7x } & = & 7 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 7 \color{blue}{+3} \\\Leftrightarrow &-20x & = &10\\\Leftrightarrow & \color{red}{-20}x & = &10\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{10}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+9}& = & 9 \color{red}{ +14x } \\\Leftrightarrow & 5x \color{red}{+9}\color{blue}{-9-14x } & = & 9 \color{red}{ +14x }\color{blue}{-9-14x } \\\Leftrightarrow & 5x \color{blue}{-14x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-10}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10-x } & = & 8 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 8 \color{blue}{+10} \\\Leftrightarrow &-3x & = &18\\\Leftrightarrow & \color{red}{-3}x & = &18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{18}{-3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-1}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1-x } & = & 9 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &-12x & = &10\\\Leftrightarrow & \color{red}{-12}x & = &10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+4}& = & -6 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4-14x } & = & -6 \color{red}{ +14x }\color{blue}{-4-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & -6 \color{blue}{-4} \\\Leftrightarrow &-x & = &-10\\\Leftrightarrow & \color{red}{-}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-10}{-1} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+6}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+6}\color{blue}{-6-x } & = & -6 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -6 \color{blue}{-6} \\\Leftrightarrow &-11x & = &-12\\\Leftrightarrow & \color{red}{-11}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+3}& = & 5 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+3}\color{blue}{-3+2x } & = & 5 \color{red}{ -2x }\color{blue}{-3+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 5 \color{blue}{-3} \\\Leftrightarrow &17x & = &2\\\Leftrightarrow & \color{red}{17}x & = &2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)