Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-x } & = & 9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 9 \color{blue}{+9} \\\Leftrightarrow &-14x & = &18\\\Leftrightarrow & \color{red}{-14}x & = &18\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{18}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+4}& = & 2 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4+13x } & = & 2 \color{red}{ -13x }\color{blue}{-4+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 2 \color{blue}{-4} \\\Leftrightarrow &24x & = &-2\\\Leftrightarrow & \color{red}{24}x & = &-2\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-2}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-1}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1-x } & = & -6 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -6 \color{blue}{+1} \\\Leftrightarrow &5x & = &-5\\\Leftrightarrow & \color{red}{5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-5}{5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-15}& = & 13 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-15}\color{blue}{+15+11x } & = & 13 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 13 \color{blue}{+15} \\\Leftrightarrow &23x & = &28\\\Leftrightarrow & \color{red}{23}x & = &28\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{28}{23} \\\Leftrightarrow & \color{green}{ x = \frac{28}{23} } & & \\ & V = \left\{ \frac{28}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-13}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13+13x } & = & -5 \color{red}{ -13x }\color{blue}{+13+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -5 \color{blue}{+13} \\\Leftrightarrow &27x & = &8\\\Leftrightarrow & \color{red}{27}x & = &8\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{8}{27} \\\Leftrightarrow & \color{green}{ x = \frac{8}{27} } & & \\ & V = \left\{ \frac{8}{27} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-11}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-x } & = & -8 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -8 \color{blue}{+11} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{-3}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3-11x } & = & 7 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 7 \color{blue}{+3} \\\Leftrightarrow &-18x & = &10\\\Leftrightarrow & \color{red}{-18}x & = &10\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{10}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-13}& = & 12 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13+5x } & = & 12 \color{red}{ -5x }\color{blue}{+13+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & 12 \color{blue}{+13} \\\Leftrightarrow &16x & = &25\\\Leftrightarrow & \color{red}{16}x & = &25\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{25}{16} \\\Leftrightarrow & \color{green}{ x = \frac{25}{16} } & & \\ & V = \left\{ \frac{25}{16} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{+2}& = & -15 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{+2}\color{blue}{-2-4x } & = & -15 \color{red}{ +4x }\color{blue}{-2-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & -15 \color{blue}{-2} \\\Leftrightarrow &-x & = &-17\\\Leftrightarrow & \color{red}{-}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-17}{-1} \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-2}& = & -10 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2+11x } & = & -10 \color{red}{ -11x }\color{blue}{+2+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & -10 \color{blue}{+2} \\\Leftrightarrow &20x & = &-8\\\Leftrightarrow & \color{red}{20}x & = &-8\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-8}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-4}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4-13x } & = & -7 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & -7 \color{blue}{+4} \\\Leftrightarrow &-10x & = &-3\\\Leftrightarrow & \color{red}{-10}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{10} } & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+10}& = & -4 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10-11x } & = & -4 \color{red}{ +11x }\color{blue}{-10-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & -4 \color{blue}{-10} \\\Leftrightarrow &-6x & = &-14\\\Leftrightarrow & \color{red}{-6}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-14}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)