Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-15}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15-13x } & = & 9 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & 9 \color{blue}{+15} \\\Leftrightarrow &-18x & = &24\\\Leftrightarrow & \color{red}{-18}x & = &24\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{24}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-2}& = & -2 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2+5x } & = & -2 \color{red}{ -5x }\color{blue}{+2+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -2 \color{blue}{+2} \\\Leftrightarrow &16x & = &0\\\Leftrightarrow & \color{red}{16}x & = &0\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{0}{16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+11}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-x } & = & 14 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 14 \color{blue}{-11} \\\Leftrightarrow &-14x & = &3\\\Leftrightarrow & \color{red}{-14}x & = &3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+4}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4-x } & = & -15 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -15 \color{blue}{-4} \\\Leftrightarrow &-7x & = &-19\\\Leftrightarrow & \color{red}{-7}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{19}{7} } & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-14}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14-x } & = & -13 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -13 \color{blue}{+14} \\\Leftrightarrow &7x & = &1\\\Leftrightarrow & \color{red}{7}x & = &1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-15}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15+13x } & = & 14 \color{red}{ -13x }\color{blue}{+15+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 14 \color{blue}{+15} \\\Leftrightarrow &27x & = &29\\\Leftrightarrow & \color{red}{27}x & = &29\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{29}{27} \\\Leftrightarrow & \color{green}{ x = \frac{29}{27} } & & \\ & V = \left\{ \frac{29}{27} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-2}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-x } & = & -2 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -2 \color{blue}{+2} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12-x } & = & -8 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -8 \color{blue}{+12} \\\Leftrightarrow &13x & = &4\\\Leftrightarrow & \color{red}{13}x & = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-15}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-15}\color{blue}{+15-7x } & = & -2 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &8x & = &13\\\Leftrightarrow & \color{red}{8}x & = &13\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{13}{8} \\\Leftrightarrow & \color{green}{ x = \frac{13}{8} } & & \\ & V = \left\{ \frac{13}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+1}& = & 14 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{+1}\color{blue}{-1-12x } & = & 14 \color{red}{ +12x }\color{blue}{-1-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & 14 \color{blue}{-1} \\\Leftrightarrow &-x & = &13\\\Leftrightarrow & \color{red}{-}x & = &13\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{13}{-1} \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+4}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4-x } & = & 10 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 10 \color{blue}{-4} \\\Leftrightarrow &-16x & = &6\\\Leftrightarrow & \color{red}{-16}x & = &6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{-1}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-1}\color{blue}{+1-x } & = & -15 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -15 \color{blue}{+1} \\\Leftrightarrow &-3x & = &-14\\\Leftrightarrow & \color{red}{-3}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-14}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{14}{3} } & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)