Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+4}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & 5x \color{red}{+4}\color{blue}{-4-13x } & = & 5 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & 5x \color{blue}{-13x } & = & 5 \color{blue}{-4} \\\Leftrightarrow &-8x & = &1\\\Leftrightarrow & \color{red}{-8}x & = &1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-9}& = & -14 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9+5x } & = & -14 \color{red}{ -5x }\color{blue}{+9+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -14 \color{blue}{+9} \\\Leftrightarrow &16x & = &-5\\\Leftrightarrow & \color{red}{16}x & = &-5\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-5}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{16} } & & \\ & V = \left\{ \frac{-5}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+6}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6-11x } & = & 3 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & -8x \color{blue}{-11x } & = & 3 \color{blue}{-6} \\\Leftrightarrow &-19x & = &-3\\\Leftrightarrow & \color{red}{-19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-11}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11-x } & = & 15 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & 15 \color{blue}{+11} \\\Leftrightarrow &14x & = &26\\\Leftrightarrow & \color{red}{14}x & = &26\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{26}{14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+6}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-11x } & = & -1 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -1 \color{blue}{-6} \\\Leftrightarrow &-16x & = &-7\\\Leftrightarrow & \color{red}{-16}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-7}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{16} } & & \\ & V = \left\{ \frac{7}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+8}& = & -2 \color{red}{ +10x } \\\Leftrightarrow & -13x \color{red}{+8}\color{blue}{-8-10x } & = & -2 \color{red}{ +10x }\color{blue}{-8-10x } \\\Leftrightarrow & -13x \color{blue}{-10x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &-23x & = &-10\\\Leftrightarrow & \color{red}{-23}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-10}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{10}{23} } & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+11}& = & -14 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{+11}\color{blue}{-11+9x } & = & -14 \color{red}{ -9x }\color{blue}{-11+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &23x & = &-25\\\Leftrightarrow & \color{red}{23}x & = &-25\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-25}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{23} } & & \\ & V = \left\{ \frac{-25}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-6}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6-x } & = & -12 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -12 \color{blue}{+6} \\\Leftrightarrow &13x & = &-6\\\Leftrightarrow & \color{red}{13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-2}& = & 7 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2-10x } & = & 7 \color{red}{ +10x }\color{blue}{+2-10x } \\\Leftrightarrow & 7x \color{blue}{-10x } & = & 7 \color{blue}{+2} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-x } & = & -3 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &-6x & = &-9\\\Leftrightarrow & \color{red}{-6}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+13}& = & 6 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13-9x } & = & 6 \color{red}{ +9x }\color{blue}{-13-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & 6 \color{blue}{-13} \\\Leftrightarrow &-x & = &-7\\\Leftrightarrow & \color{red}{-}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-7}{-1} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-3}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3-7x } & = & -2 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &-20x & = &1\\\Leftrightarrow & \color{red}{-20}x & = &1\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{1}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{20} } & & \\ & V = \left\{ \frac{-1}{20} \right\} & \\\end{align}\)