Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+13}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13-x } & = & 8 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 8 \color{blue}{-13} \\\Leftrightarrow &-9x & = &-5\\\Leftrightarrow & \color{red}{-9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{-2}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2-13x } & = & -6 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & -6 \color{blue}{+2} \\\Leftrightarrow &-4x & = &-4\\\Leftrightarrow & \color{red}{-4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-4}{-4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+10}& = & -12 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+10}\color{blue}{-10-5x } & = & -12 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -12 \color{blue}{-10} \\\Leftrightarrow &-9x & = &-22\\\Leftrightarrow & \color{red}{-9}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-22}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{22}{9} } & & \\ & V = \left\{ \frac{22}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+14}& = & 4 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14-3x } & = & 4 \color{red}{ +3x }\color{blue}{-14-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-10\\\Leftrightarrow & \color{red}{-5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-10}{-5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-4}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-4}\color{blue}{+4-x } & = & 10 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 10 \color{blue}{+4} \\\Leftrightarrow &-3x & = &14\\\Leftrightarrow & \color{red}{-3}x & = &14\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{14}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{3} } & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-2}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-2}\color{blue}{+2-x } & = & -1 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -1 \color{blue}{+2} \\\Leftrightarrow &-3x & = &1\\\Leftrightarrow & \color{red}{-3}x & = &1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+8}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+8}\color{blue}{-8-x } & = & -3 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -3 \color{blue}{-8} \\\Leftrightarrow &-10x & = &-11\\\Leftrightarrow & \color{red}{-10}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-11}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{10} } & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-6}& = & 12 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{-6}\color{blue}{+6-3x } & = & 12 \color{red}{ +3x }\color{blue}{+6-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & 12 \color{blue}{+6} \\\Leftrightarrow &-14x & = &18\\\Leftrightarrow & \color{red}{-14}x & = &18\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{18}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-14}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14-x } & = & -9 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -9 \color{blue}{+14} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{-8}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8-x } & = & -11 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -11 \color{blue}{+8} \\\Leftrightarrow &-10x & = &-3\\\Leftrightarrow & \color{red}{-10}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{10} } & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+11}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11-x } & = & 12 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 12 \color{blue}{-11} \\\Leftrightarrow &-6x & = &1\\\Leftrightarrow & \color{red}{-6}x & = &1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{-7}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7-13x } & = & 8 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 8 \color{blue}{+7} \\\Leftrightarrow &-19x & = &15\\\Leftrightarrow & \color{red}{-19}x & = &15\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{15}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{19} } & & \\ & V = \left\{ \frac{-15}{19} \right\} & \\\end{align}\)