Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+9}\color{blue}{-9-x } & = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{-15}& = & -12 \color{red}{ -5x } \\\Leftrightarrow & 13x \color{red}{-15}\color{blue}{+15+5x } & = & -12 \color{red}{ -5x }\color{blue}{+15+5x } \\\Leftrightarrow & 13x \color{blue}{+5x } & = & -12 \color{blue}{+15} \\\Leftrightarrow &18x & = &3\\\Leftrightarrow & \color{red}{18}x & = &3\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{3}{18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{+10}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-x } & = & 3 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 3 \color{blue}{-10} \\\Leftrightarrow &-16x & = &-7\\\Leftrightarrow & \color{red}{-16}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-7}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{16} } & & \\ & V = \left\{ \frac{7}{16} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-10}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-10}\color{blue}{+10-13x } & = & -13 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & -13 \color{blue}{+10} \\\Leftrightarrow &-17x & = &-3\\\Leftrightarrow & \color{red}{-17}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{-10}& = & -12 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10+3x } & = & -12 \color{red}{ -3x }\color{blue}{+10+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -12 \color{blue}{+10} \\\Leftrightarrow &10x & = &-2\\\Leftrightarrow & \color{red}{10}x & = &-2\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-2}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-2}& = & -1 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{-2}\color{blue}{+2-3x } & = & -1 \color{red}{ +3x }\color{blue}{+2-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & -1 \color{blue}{+2} \\\Leftrightarrow &5x & = &1\\\Leftrightarrow & \color{red}{5}x & = &1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+11}& = & 13 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11+2x } & = & 13 \color{red}{ -2x }\color{blue}{-11+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &5x & = &2\\\Leftrightarrow & \color{red}{5}x & = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+14}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+14}\color{blue}{-14-x } & = & -15 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -15 \color{blue}{-14} \\\Leftrightarrow &-16x & = &-29\\\Leftrightarrow & \color{red}{-16}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-29}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{29}{16} } & & \\ & V = \left\{ \frac{29}{16} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+10}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10-x } & = & 15 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 15 \color{blue}{-10} \\\Leftrightarrow &6x & = &5\\\Leftrightarrow & \color{red}{6}x & = &5\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{5}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+2}& = & 12 \color{red}{ -9x } \\\Leftrightarrow & 7x \color{red}{+2}\color{blue}{-2+9x } & = & 12 \color{red}{ -9x }\color{blue}{-2+9x } \\\Leftrightarrow & 7x \color{blue}{+9x } & = & 12 \color{blue}{-2} \\\Leftrightarrow &16x & = &10\\\Leftrightarrow & \color{red}{16}x & = &10\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{10}{16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-2}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2-13x } & = & 8 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & 8 \color{blue}{+2} \\\Leftrightarrow &2x & = &10\\\Leftrightarrow & \color{red}{2}x & = &10\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{10}{2} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{-10}& = & -5 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-10}\color{blue}{+10+11x } & = & -5 \color{red}{ -11x }\color{blue}{+10+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -5 \color{blue}{+10} \\\Leftrightarrow &14x & = &5\\\Leftrightarrow & \color{red}{14}x & = &5\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{5}{14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)