Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-12}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12-13x } & = & 8 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 8 \color{blue}{+12} \\\Leftrightarrow &-25x & = &20\\\Leftrightarrow & \color{red}{-25}x & = &20\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{20}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{+15}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15-x } & = & -11 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -11 \color{blue}{-15} \\\Leftrightarrow &12x & = &-26\\\Leftrightarrow & \color{red}{12}x & = &-26\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-26}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+3}& = & -15 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3-9x } & = & -15 \color{red}{ +9x }\color{blue}{-3-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & -15 \color{blue}{-3} \\\Leftrightarrow &-x & = &-18\\\Leftrightarrow & \color{red}{-}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-18}{-1} \\\Leftrightarrow & \color{green}{ x = 18 } & & \\ & V = \left\{ 18 \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+2}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2+11x } & = & -13 \color{red}{ -11x }\color{blue}{-2+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -13 \color{blue}{-2} \\\Leftrightarrow &17x & = &-15\\\Leftrightarrow & \color{red}{17}x & = &-15\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-15}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{17} } & & \\ & V = \left\{ \frac{-15}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-11}& = & 8 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-6x } & = & 8 \color{red}{ +6x }\color{blue}{+11-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 8 \color{blue}{+11} \\\Leftrightarrow &-17x & = &19\\\Leftrightarrow & \color{red}{-17}x & = &19\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{19}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{17} } & & \\ & V = \left\{ \frac{-19}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-8}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8-x } & = & 2 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 2 \color{blue}{+8} \\\Leftrightarrow &-12x & = &10\\\Leftrightarrow & \color{red}{-12}x & = &10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+1}& = & 6 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+1}\color{blue}{-1-6x } & = & 6 \color{red}{ +6x }\color{blue}{-1-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-1}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1-9x } & = & -12 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & -12 \color{blue}{+1} \\\Leftrightarrow &-20x & = &-11\\\Leftrightarrow & \color{red}{-20}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-11}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{11}{20} } & & \\ & V = \left\{ \frac{11}{20} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+13}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+13}\color{blue}{-13-x } & = & 15 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &-14x & = &2\\\Leftrightarrow & \color{red}{-14}x & = &2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+12}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+12}\color{blue}{-12-13x } & = & 13 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 13 \color{blue}{-12} \\\Leftrightarrow &-28x & = &1\\\Leftrightarrow & \color{red}{-28}x & = &1\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{1}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{28} } & & \\ & V = \left\{ \frac{-1}{28} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-10}& = & 13 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{-10}\color{blue}{+10+3x } & = & 13 \color{red}{ -3x }\color{blue}{+10+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &7x & = &23\\\Leftrightarrow & \color{red}{7}x & = &23\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{23}{7} \\\Leftrightarrow & \color{green}{ x = \frac{23}{7} } & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{+8}& = & -13 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+8}\color{blue}{-8-5x } & = & -13 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -13 \color{blue}{-8} \\\Leftrightarrow &-17x & = &-21\\\Leftrightarrow & \color{red}{-17}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-21}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{21}{17} } & & \\ & V = \left\{ \frac{21}{17} \right\} & \\\end{align}\)