Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-7}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7-x } & = & -9 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -9 \color{blue}{+7} \\\Leftrightarrow &11x & = &-2\\\Leftrightarrow & \color{red}{11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+8}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-7x } & = & 4 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 4 \color{blue}{-8} \\\Leftrightarrow &-17x & = &-4\\\Leftrightarrow & \color{red}{-17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+4}& = & 9 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{+4}\color{blue}{-4+11x } & = & 9 \color{red}{ -11x }\color{blue}{-4+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 9 \color{blue}{-4} \\\Leftrightarrow &20x & = &5\\\Leftrightarrow & \color{red}{20}x & = &5\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{5}{20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{-15}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-x } & = & 13 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 13 \color{blue}{+15} \\\Leftrightarrow &-8x & = &28\\\Leftrightarrow & \color{red}{-8}x & = &28\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{28}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-8}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8-9x } & = & 12 \color{red}{ +9x }\color{blue}{+8-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 12 \color{blue}{+8} \\\Leftrightarrow &-17x & = &20\\\Leftrightarrow & \color{red}{-17}x & = &20\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{20}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{17} } & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-1}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-1}\color{blue}{+1-9x } & = & -12 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & -12 \color{blue}{+1} \\\Leftrightarrow &-x & = &-11\\\Leftrightarrow & \color{red}{-}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-11}{-1} \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-1}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1-7x } & = & -4 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & -x \color{blue}{-7x } & = & -4 \color{blue}{+1} \\\Leftrightarrow &-8x & = &-3\\\Leftrightarrow & \color{red}{-8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+8}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8-x } & = & 5 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & 5 \color{blue}{-8} \\\Leftrightarrow &8x & = &-3\\\Leftrightarrow & \color{red}{8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-3}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-15}& = & -1 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15-5x } & = & -1 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & -1 \color{blue}{+15} \\\Leftrightarrow &3x & = &14\\\Leftrightarrow & \color{red}{3}x & = &14\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{14}{3} \\\Leftrightarrow & \color{green}{ x = \frac{14}{3} } & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-7}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7-13x } & = & -10 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -10 \color{blue}{+7} \\\Leftrightarrow &-19x & = &-3\\\Leftrightarrow & \color{red}{-19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-11}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-11x } & = & -15 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -15 \color{blue}{+11} \\\Leftrightarrow &-16x & = &-4\\\Leftrightarrow & \color{red}{-16}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{+14}& = & 2 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{+14}\color{blue}{-14-9x } & = & 2 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & 2 \color{blue}{-14} \\\Leftrightarrow &-x & = &-12\\\Leftrightarrow & \color{red}{-}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-12}{-1} \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)