Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{+11}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11-x } & = & -2 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & -2 \color{blue}{-11} \\\Leftrightarrow &6x & = &-13\\\Leftrightarrow & \color{red}{6}x & = &-13\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-13}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-15}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-15}\color{blue}{+15-x } & = & -7 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -7 \color{blue}{+15} \\\Leftrightarrow &-4x & = &8\\\Leftrightarrow & \color{red}{-4}x & = &8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{8}{-4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-8}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-8}\color{blue}{+8-x } & = & 2 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 2 \color{blue}{+8} \\\Leftrightarrow &-13x & = &10\\\Leftrightarrow & \color{red}{-13}x & = &10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{-10}& = & 13 \color{red}{ +11x } \\\Leftrightarrow & -8x \color{red}{-10}\color{blue}{+10-11x } & = & 13 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & -8x \color{blue}{-11x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &-19x & = &23\\\Leftrightarrow & \color{red}{-19}x & = &23\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{23}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{19} } & & \\ & V = \left\{ \frac{-23}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+3}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+3}\color{blue}{-3-x } & = & 4 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 4 \color{blue}{-3} \\\Leftrightarrow &-3x & = &1\\\Leftrightarrow & \color{red}{-3}x & = &1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+8}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8-9x } & = & -7 \color{red}{ +9x }\color{blue}{-8-9x } \\\Leftrightarrow & 11x \color{blue}{-9x } & = & -7 \color{blue}{-8} \\\Leftrightarrow &2x & = &-15\\\Leftrightarrow & \color{red}{2}x & = &-15\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-15}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{2} } & & \\ & V = \left\{ \frac{-15}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{+2}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+2}\color{blue}{-2-x } & = & 1 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 1 \color{blue}{-2} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+5}& = & -6 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+5}\color{blue}{-5-9x } & = & -6 \color{red}{ +9x }\color{blue}{-5-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -6 \color{blue}{-5} \\\Leftrightarrow &-17x & = &-11\\\Leftrightarrow & \color{red}{-17}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-11}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{11}{17} } & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+7}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7-13x } & = & -12 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &2x & = &-19\\\Leftrightarrow & \color{red}{2}x & = &-19\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-19}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{2} } & & \\ & V = \left\{ \frac{-19}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-11}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-x } & = & -4 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -4 \color{blue}{+11} \\\Leftrightarrow &-6x & = &7\\\Leftrightarrow & \color{red}{-6}x & = &7\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{7}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-14}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14-x } & = & -6 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -6 \color{blue}{+14} \\\Leftrightarrow &-3x & = &8\\\Leftrightarrow & \color{red}{-3}x & = &8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+5}& = & 4 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+5}\color{blue}{-5+4x } & = & 4 \color{red}{ -4x }\color{blue}{-5+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &13x & = &-1\\\Leftrightarrow & \color{red}{13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)