Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{-14}& = & -9 \color{red}{ +12x } \\\Leftrightarrow & 5x \color{red}{-14}\color{blue}{+14-12x } & = & -9 \color{red}{ +12x }\color{blue}{+14-12x } \\\Leftrightarrow & 5x \color{blue}{-12x } & = & -9 \color{blue}{+14} \\\Leftrightarrow &-7x & = &5\\\Leftrightarrow & \color{red}{-7}x & = &5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-2}& = & 10 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-2}\color{blue}{+2+11x } & = & 10 \color{red}{ -11x }\color{blue}{+2+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & 10 \color{blue}{+2} \\\Leftrightarrow &14x & = &12\\\Leftrightarrow & \color{red}{14}x & = &12\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{12}{14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+1}& = & -1 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{+1}\color{blue}{-1+5x } & = & -1 \color{red}{ -5x }\color{blue}{-1+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -1 \color{blue}{-1} \\\Leftrightarrow &16x & = &-2\\\Leftrightarrow & \color{red}{16}x & = &-2\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-2}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{-4}& = & -14 \color{red}{ -7x } \\\Leftrightarrow & -x \color{red}{-4}\color{blue}{+4+7x } & = & -14 \color{red}{ -7x }\color{blue}{+4+7x } \\\Leftrightarrow & -x \color{blue}{+7x } & = & -14 \color{blue}{+4} \\\Leftrightarrow &6x & = &-10\\\Leftrightarrow & \color{red}{6}x & = &-10\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-10}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{-10}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10-x } & = & 14 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 14 \color{blue}{+10} \\\Leftrightarrow &-7x & = &24\\\Leftrightarrow & \color{red}{-7}x & = &24\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{24}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{7} } & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{-1}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-1}\color{blue}{+1-x } & = & -10 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -10 \color{blue}{+1} \\\Leftrightarrow &3x & = &-9\\\Leftrightarrow & \color{red}{3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-9}{3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-1}& = & 3 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-3x } & = & 3 \color{red}{ +3x }\color{blue}{+1-3x } \\\Leftrightarrow & -8x \color{blue}{-3x } & = & 3 \color{blue}{+1} \\\Leftrightarrow &-11x & = &4\\\Leftrightarrow & \color{red}{-11}x & = &4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-14}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14-13x } & = & -8 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & -8 \color{blue}{+14} \\\Leftrightarrow &-15x & = &6\\\Leftrightarrow & \color{red}{-15}x & = &6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-2}& = & -5 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2+6x } & = & -5 \color{red}{ -6x }\color{blue}{+2+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &19x & = &-3\\\Leftrightarrow & \color{red}{19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-3}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{19} } & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-12}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-12}\color{blue}{+12-x } & = & 5 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 5 \color{blue}{+12} \\\Leftrightarrow &x & = &17\\\Leftrightarrow & \color{red}{}x & = &17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 17 \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+11}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11-7x } & = & 12 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 12 \color{blue}{-11} \\\Leftrightarrow &-13x & = &1\\\Leftrightarrow & \color{red}{-13}x & = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-7}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-7}\color{blue}{+7-x } & = & -12 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -12 \color{blue}{+7} \\\Leftrightarrow &-9x & = &-5\\\Leftrightarrow & \color{red}{-9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)