Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-11}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-x } & = & -8 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -8 \color{blue}{+11} \\\Leftrightarrow &-6x & = &3\\\Leftrightarrow & \color{red}{-6}x & = &3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-7}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7-7x } & = & 10 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & 10 \color{blue}{+7} \\\Leftrightarrow &-10x & = &17\\\Leftrightarrow & \color{red}{-10}x & = &17\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{17}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{10} } & & \\ & V = \left\{ \frac{-17}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-7}& = & 4 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7-4x } & = & 4 \color{red}{ +4x }\color{blue}{+7-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & 4 \color{blue}{+7} \\\Leftrightarrow &-7x & = &11\\\Leftrightarrow & \color{red}{-7}x & = &11\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{11}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{-8}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8-5x } & = & -11 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & -11 \color{blue}{+8} \\\Leftrightarrow &-x & = &-3\\\Leftrightarrow & \color{red}{-}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-3}{-1} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-2}\color{blue}{+2-x } & = & -3 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -3 \color{blue}{+2} \\\Leftrightarrow &-6x & = &-1\\\Leftrightarrow & \color{red}{-6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-15}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15-13x } & = & 9 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & 9 \color{blue}{+15} \\\Leftrightarrow &-18x & = &24\\\Leftrightarrow & \color{red}{-18}x & = &24\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{24}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{+12}& = & 9 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+12}\color{blue}{-12+11x } & = & 9 \color{red}{ -11x }\color{blue}{-12+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &15x & = &-3\\\Leftrightarrow & \color{red}{15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-3}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-6}& = & -9 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6-4x } & = & -9 \color{red}{ +4x }\color{blue}{+6-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & -9 \color{blue}{+6} \\\Leftrightarrow &5x & = &-3\\\Leftrightarrow & \color{red}{5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+3}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3-11x } & = & 12 \color{red}{ +11x }\color{blue}{-3-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 12 \color{blue}{-3} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-8}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8-9x } & = & 12 \color{red}{ +9x }\color{blue}{+8-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 12 \color{blue}{+8} \\\Leftrightarrow &-17x & = &20\\\Leftrightarrow & \color{red}{-17}x & = &20\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{20}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{17} } & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-5}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-5}\color{blue}{+5-x } & = & -14 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -14 \color{blue}{+5} \\\Leftrightarrow &-12x & = &-9\\\Leftrightarrow & \color{red}{-12}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-9}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+10}& = & -4 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+10}\color{blue}{-10+11x } & = & -4 \color{red}{ -11x }\color{blue}{-10+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -4 \color{blue}{-10} \\\Leftrightarrow &17x & = &-14\\\Leftrightarrow & \color{red}{17}x & = &-14\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-14}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{17} } & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)