Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+1}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & x \color{red}{+1}\color{blue}{-1-11x } & = & -8 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & x \color{blue}{-11x } & = & -8 \color{blue}{-1} \\\Leftrightarrow &-10x & = &-9\\\Leftrightarrow & \color{red}{-10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-7}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-7}\color{blue}{+7-x } & = & -5 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -5 \color{blue}{+7} \\\Leftrightarrow &-10x & = &2\\\Leftrightarrow & \color{red}{-10}x & = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+7}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7-11x } & = & -9 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & 14x \color{blue}{-11x } & = & -9 \color{blue}{-7} \\\Leftrightarrow &3x & = &-16\\\Leftrightarrow & \color{red}{3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-16}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-2}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-2}\color{blue}{+2-x } & = & -8 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -8 \color{blue}{+2} \\\Leftrightarrow &-13x & = &-6\\\Leftrightarrow & \color{red}{-13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-13}& = & 12 \color{red}{ +2x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13-2x } & = & 12 \color{red}{ +2x }\color{blue}{+13-2x } \\\Leftrightarrow & 11x \color{blue}{-2x } & = & 12 \color{blue}{+13} \\\Leftrightarrow &9x & = &25\\\Leftrightarrow & \color{red}{9}x & = &25\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{25}{9} \\\Leftrightarrow & \color{green}{ x = \frac{25}{9} } & & \\ & V = \left\{ \frac{25}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+2}& = & -6 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2+2x } & = & -6 \color{red}{ -2x }\color{blue}{-2+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & -6 \color{blue}{-2} \\\Leftrightarrow &13x & = &-8\\\Leftrightarrow & \color{red}{13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+5}& = & -3 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+5}\color{blue}{-5+4x } & = & -3 \color{red}{ -4x }\color{blue}{-5+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &13x & = &-8\\\Leftrightarrow & \color{red}{13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{-14}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14-x } & = & -5 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -5 \color{blue}{+14} \\\Leftrightarrow &-4x & = &9\\\Leftrightarrow & \color{red}{-4}x & = &9\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{9}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+10}& = & 12 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-3x } & = & 12 \color{red}{ +3x }\color{blue}{-10-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & 12 \color{blue}{-10} \\\Leftrightarrow &-14x & = &2\\\Leftrightarrow & \color{red}{-14}x & = &2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-7}& = & -15 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7+9x } & = & -15 \color{red}{ -9x }\color{blue}{+7+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -15 \color{blue}{+7} \\\Leftrightarrow &19x & = &-8\\\Leftrightarrow & \color{red}{19}x & = &-8\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-8}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{19} } & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-1}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & 15 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &-15x & = &16\\\Leftrightarrow & \color{red}{-15}x & = &16\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{16}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{15} } & & \\ & V = \left\{ \frac{-16}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+3}& = & -10 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{+3}\color{blue}{-3+10x } & = & -10 \color{red}{ -10x }\color{blue}{-3+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & -10 \color{blue}{-3} \\\Leftrightarrow &17x & = &-13\\\Leftrightarrow & \color{red}{17}x & = &-13\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-13}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{17} } & & \\ & V = \left\{ \frac{-13}{17} \right\} & \\\end{align}\)