Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+5}& = & 10 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+5}\color{blue}{-5+4x } & = & 10 \color{red}{ -4x }\color{blue}{-5+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 10 \color{blue}{-5} \\\Leftrightarrow &9x & = &5\\\Leftrightarrow & \color{red}{9}x & = &5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-9}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-x } & = & 10 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &-14x & = &19\\\Leftrightarrow & \color{red}{-14}x & = &19\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{19}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{14} } & & \\ & V = \left\{ \frac{-19}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-12}& = & 13 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12-3x } & = & 13 \color{red}{ +3x }\color{blue}{+12-3x } \\\Leftrightarrow & -8x \color{blue}{-3x } & = & 13 \color{blue}{+12} \\\Leftrightarrow &-11x & = &25\\\Leftrightarrow & \color{red}{-11}x & = &25\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{25}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{11} } & & \\ & V = \left\{ \frac{-25}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-13}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13-11x } & = & 6 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 6 \color{blue}{+13} \\\Leftrightarrow &-5x & = &19\\\Leftrightarrow & \color{red}{-5}x & = &19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{5} } & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-11}& = & -5 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11+15x } & = & -5 \color{red}{ -15x }\color{blue}{+11+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & -5 \color{blue}{+11} \\\Leftrightarrow &23x & = &6\\\Leftrightarrow & \color{red}{23}x & = &6\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{6}{23} \\\Leftrightarrow & \color{green}{ x = \frac{6}{23} } & & \\ & V = \left\{ \frac{6}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+10}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-13x } & = & -2 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & -2 \color{blue}{-10} \\\Leftrightarrow &-18x & = &-12\\\Leftrightarrow & \color{red}{-18}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-12}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-12}& = & 13 \color{red}{ -4x } \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12+4x } & = & 13 \color{red}{ -4x }\color{blue}{+12+4x } \\\Leftrightarrow & x \color{blue}{+4x } & = & 13 \color{blue}{+12} \\\Leftrightarrow &5x & = &25\\\Leftrightarrow & \color{red}{5}x & = &25\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{25}{5} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+4}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-x } & = & -14 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &-10x & = &-18\\\Leftrightarrow & \color{red}{-10}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-18}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-7}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-7}\color{blue}{+7-x } & = & 12 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 12 \color{blue}{+7} \\\Leftrightarrow &3x & = &19\\\Leftrightarrow & \color{red}{3}x & = &19\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{19}{3} \\\Leftrightarrow & \color{green}{ x = \frac{19}{3} } & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-3}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-3}\color{blue}{+3-5x } & = & -15 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -15 \color{blue}{+3} \\\Leftrightarrow &-9x & = &-12\\\Leftrightarrow & \color{red}{-9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-14}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14-x } & = & 13 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 13 \color{blue}{+14} \\\Leftrightarrow &-14x & = &27\\\Leftrightarrow & \color{red}{-14}x & = &27\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{27}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{14} } & & \\ & V = \left\{ \frac{-27}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-14}& = & -13 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-14}\color{blue}{+14-8x } & = & -13 \color{red}{ +8x }\color{blue}{+14-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -13 \color{blue}{+14} \\\Leftrightarrow &-23x & = &1\\\Leftrightarrow & \color{red}{-23}x & = &1\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{1}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{23} } & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)