Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-13}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{-13}\color{blue}{+13-11x } & = & -6 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & -6 \color{blue}{+13} \\\Leftrightarrow &-13x & = &7\\\Leftrightarrow & \color{red}{-13}x & = &7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-1}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1-x } & = & 11 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 11 \color{blue}{+1} \\\Leftrightarrow &-14x & = &12\\\Leftrightarrow & \color{red}{-14}x & = &12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-1}& = & -7 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-1}\color{blue}{+1-10x } & = & -7 \color{red}{ +10x }\color{blue}{+1-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & -7 \color{blue}{+1} \\\Leftrightarrow &-13x & = &-6\\\Leftrightarrow & \color{red}{-13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-2}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-2}\color{blue}{+2-x } & = & 10 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 10 \color{blue}{+2} \\\Leftrightarrow &-15x & = &12\\\Leftrightarrow & \color{red}{-15}x & = &12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+14}& = & -3 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+14}\color{blue}{-14+8x } & = & -3 \color{red}{ -8x }\color{blue}{-14+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &17x & = &-17\\\Leftrightarrow & \color{red}{17}x & = &-17\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-17}{17} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-14}& = & -9 \color{red}{ +14x } \\\Leftrightarrow & -x \color{red}{-14}\color{blue}{+14-14x } & = & -9 \color{red}{ +14x }\color{blue}{+14-14x } \\\Leftrightarrow & -x \color{blue}{-14x } & = & -9 \color{blue}{+14} \\\Leftrightarrow &-15x & = &5\\\Leftrightarrow & \color{red}{-15}x & = &5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+14}& = & -12 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14+2x } & = & -12 \color{red}{ -2x }\color{blue}{-14+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & -12 \color{blue}{-14} \\\Leftrightarrow &5x & = &-26\\\Leftrightarrow & \color{red}{5}x & = &-26\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-26}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{5} } & & \\ & V = \left\{ \frac{-26}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+1}& = & 4 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1-14x } & = & 4 \color{red}{ +14x }\color{blue}{-1-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 4 \color{blue}{-1} \\\Leftrightarrow &-23x & = &3\\\Leftrightarrow & \color{red}{-23}x & = &3\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{3}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{23} } & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{-3}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3-x } & = & -11 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -11 \color{blue}{+3} \\\Leftrightarrow &13x & = &-8\\\Leftrightarrow & \color{red}{13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-6}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-x } & = & -2 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -2 \color{blue}{+6} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+1}& = & 3 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1-14x } & = & 3 \color{red}{ +14x }\color{blue}{-1-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 3 \color{blue}{-1} \\\Leftrightarrow &-23x & = &2\\\Leftrightarrow & \color{red}{-23}x & = &2\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{2}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{23} } & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{-6}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-6}\color{blue}{+6-x } & = & 10 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 10 \color{blue}{+6} \\\Leftrightarrow &-3x & = &16\\\Leftrightarrow & \color{red}{-3}x & = &16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)