Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+12}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12-x } & = & -14 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & -14 \color{blue}{-12} \\\Leftrightarrow &4x & = &-26\\\Leftrightarrow & \color{red}{4}x & = &-26\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-26}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{2} } & & \\ & V = \left\{ \frac{-13}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+7}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+7}\color{blue}{-7+11x } & = & 2 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 2 \color{blue}{-7} \\\Leftrightarrow &15x & = &-5\\\Leftrightarrow & \color{red}{15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-5}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+15}& = & 12 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15+14x } & = & 12 \color{red}{ -14x }\color{blue}{-15+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 12 \color{blue}{-15} \\\Leftrightarrow &29x & = &-3\\\Leftrightarrow & \color{red}{29}x & = &-3\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-3}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{29} } & & \\ & V = \left\{ \frac{-3}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+9}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+9}\color{blue}{-9-x } & = & 12 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 12 \color{blue}{-9} \\\Leftrightarrow &-6x & = &3\\\Leftrightarrow & \color{red}{-6}x & = &3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{-11}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-x } & = & -2 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -2 \color{blue}{+11} \\\Leftrightarrow &-7x & = &9\\\Leftrightarrow & \color{red}{-7}x & = &9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+5}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+5}\color{blue}{-5-x } & = & -15 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &-13x & = &-20\\\Leftrightarrow & \color{red}{-13}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-20}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{20}{13} } & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-5}& = & -3 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5-6x } & = & -3 \color{red}{ +6x }\color{blue}{+5-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & -3 \color{blue}{+5} \\\Leftrightarrow &-x & = &2\\\Leftrightarrow & \color{red}{-}x & = &2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{2}{-1} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-9}& = & 4 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9+10x } & = & 4 \color{red}{ -10x }\color{blue}{+9+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 4 \color{blue}{+9} \\\Leftrightarrow &21x & = &13\\\Leftrightarrow & \color{red}{21}x & = &13\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{13}{21} \\\Leftrightarrow & \color{green}{ x = \frac{13}{21} } & & \\ & V = \left\{ \frac{13}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+4}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+4}\color{blue}{-4-x } & = & -9 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -9 \color{blue}{-4} \\\Leftrightarrow &-12x & = &-13\\\Leftrightarrow & \color{red}{-12}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{12} } & & \\ & V = \left\{ \frac{13}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-4}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-4}\color{blue}{+4-11x } & = & 3 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 3 \color{blue}{+4} \\\Leftrightarrow &x & = &7\\\Leftrightarrow & \color{red}{}x & = &7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 7 \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+9}& = & -11 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9+13x } & = & -11 \color{red}{ -13x }\color{blue}{-9+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -11 \color{blue}{-9} \\\Leftrightarrow &24x & = &-20\\\Leftrightarrow & \color{red}{24}x & = &-20\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-20}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-11}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11-x } & = & 14 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 14 \color{blue}{+11} \\\Leftrightarrow &7x & = &25\\\Leftrightarrow & \color{red}{7}x & = &25\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{25}{7} \\\Leftrightarrow & \color{green}{ x = \frac{25}{7} } & & \\ & V = \left\{ \frac{25}{7} \right\} & \\\end{align}\)