Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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