Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+5}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -x \color{red}{+5}\color{blue}{-5-x } & = & 12 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -x \color{blue}{-x } & = & 12 \color{blue}{-5} \\\Leftrightarrow &-2x & = &7\\\Leftrightarrow & \color{red}{-2}x & = &7\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{7}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+15}& = & -15 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+15}\color{blue}{-15-3x } & = & -15 \color{red}{ +3x }\color{blue}{-15-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -15 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-30\\\Leftrightarrow & \color{red}{-5}x & = &-30\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-30}{-5} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-5}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5-13x } & = & -2 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -2 \color{blue}{+5} \\\Leftrightarrow &-28x & = &3\\\Leftrightarrow & \color{red}{-28}x & = &3\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{3}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{28} } & & \\ & V = \left\{ \frac{-3}{28} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-4}& = & 9 \color{red}{ +3x } \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4-3x } & = & 9 \color{red}{ +3x }\color{blue}{+4-3x } \\\Leftrightarrow & 7x \color{blue}{-3x } & = & 9 \color{blue}{+4} \\\Leftrightarrow &4x & = &13\\\Leftrightarrow & \color{red}{4}x & = &13\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{13}{4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14-x } & = & 4 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 4 \color{blue}{+14} \\\Leftrightarrow &-3x & = &18\\\Leftrightarrow & \color{red}{-3}x & = &18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{18}{-3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{+1}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+1}\color{blue}{-1-5x } & = & -8 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -8 \color{blue}{-1} \\\Leftrightarrow &-9x & = &-9\\\Leftrightarrow & \color{red}{-9}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-9}{-9} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-9}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-11x } & = & -8 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &-16x & = &1\\\Leftrightarrow & \color{red}{-16}x & = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+8}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+8}\color{blue}{-8-x } & = & -1 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -1 \color{blue}{-8} \\\Leftrightarrow &-4x & = &-9\\\Leftrightarrow & \color{red}{-4}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-9}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-11}& = & -10 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11-10x } & = & -10 \color{red}{ +10x }\color{blue}{+11-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & -10 \color{blue}{+11} \\\Leftrightarrow &-x & = &1\\\Leftrightarrow & \color{red}{-}x & = &1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{1}{-1} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+10}& = & 9 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10+13x } & = & 9 \color{red}{ -13x }\color{blue}{-10+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 9 \color{blue}{-10} \\\Leftrightarrow &20x & = &-1\\\Leftrightarrow & \color{red}{20}x & = &-1\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-1}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{20} } & & \\ & V = \left\{ \frac{-1}{20} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-6}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6-7x } & = & 10 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & 13x \color{blue}{-7x } & = & 10 \color{blue}{+6} \\\Leftrightarrow &6x & = &16\\\Leftrightarrow & \color{red}{6}x & = &16\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{16}{6} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+12}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+12}\color{blue}{-12-13x } & = & -9 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -9 \color{blue}{-12} \\\Leftrightarrow &-19x & = &-21\\\Leftrightarrow & \color{red}{-19}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-21}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{21}{19} } & & \\ & V = \left\{ \frac{21}{19} \right\} & \\\end{align}\)