Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-12}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12-x } & = & -11 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -11 \color{blue}{+12} \\\Leftrightarrow &13x & = &1\\\Leftrightarrow & \color{red}{13}x & = &1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+9}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+9}\color{blue}{-9-11x } & = & -9 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &-9x & = &-18\\\Leftrightarrow & \color{red}{-9}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-18}{-9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-11}& = & -13 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-8x } & = & -13 \color{red}{ +8x }\color{blue}{+11-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & -13 \color{blue}{+11} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-14}& = & 7 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14+5x } & = & 7 \color{red}{ -5x }\color{blue}{+14+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 7 \color{blue}{+14} \\\Leftrightarrow &11x & = &21\\\Leftrightarrow & \color{red}{11}x & = &21\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{21}{11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+8}& = & 8 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8+11x } & = & 8 \color{red}{ -11x }\color{blue}{-8+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 8 \color{blue}{-8} \\\Leftrightarrow &15x & = &0\\\Leftrightarrow & \color{red}{15}x & = &0\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{0}{15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+9}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+9}\color{blue}{-9-x } & = & -15 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &x & = &-24\\\Leftrightarrow & \color{red}{}x & = &-24\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -24 \\\Leftrightarrow & \color{green}{ x = -24 } & & \\ & V = \left\{ -24 \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-3}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3-x } & = & -4 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -4 \color{blue}{+3} \\\Leftrightarrow &-6x & = &-1\\\Leftrightarrow & \color{red}{-6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+13}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+13}\color{blue}{-13-x } & = & -5 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -5 \color{blue}{-13} \\\Leftrightarrow &-3x & = &-18\\\Leftrightarrow & \color{red}{-3}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-18}{-3} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+10}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10-11x } & = & 12 \color{red}{ +11x }\color{blue}{-10-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & 12 \color{blue}{-10} \\\Leftrightarrow &-6x & = &2\\\Leftrightarrow & \color{red}{-6}x & = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-1}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-x } & = & -5 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -5 \color{blue}{+1} \\\Leftrightarrow &-13x & = &-4\\\Leftrightarrow & \color{red}{-13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-11}& = & 7 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11+10x } & = & 7 \color{red}{ -10x }\color{blue}{+11+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &9x & = &18\\\Leftrightarrow & \color{red}{9}x & = &18\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{18}{9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{+10}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+10}\color{blue}{-10-x } & = & 3 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 3 \color{blue}{-10} \\\Leftrightarrow &7x & = &-7\\\Leftrightarrow & \color{red}{7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-7}{7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)