Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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