Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-6}& = & -1 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6-5x } & = & -1 \color{red}{ +5x }\color{blue}{+6-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & -1 \color{blue}{+6} \\\Leftrightarrow &-x & = &5\\\Leftrightarrow & \color{red}{-}x & = &5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{5}{-1} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+7}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-11x } & = & 4 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 4 \color{blue}{-7} \\\Leftrightarrow &-9x & = &-3\\\Leftrightarrow & \color{red}{-9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+11}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+11}\color{blue}{-11-x } & = & 4 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 4 \color{blue}{-11} \\\Leftrightarrow &-15x & = &-7\\\Leftrightarrow & \color{red}{-15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{+14}& = & -3 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14-14x } & = & -3 \color{red}{ +14x }\color{blue}{-14-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &-23x & = &-17\\\Leftrightarrow & \color{red}{-23}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-17}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{17}{23} } & & \\ & V = \left\{ \frac{17}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{-13}& = & -9 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{-13}\color{blue}{+13-10x } & = & -9 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -9 \color{blue}{+13} \\\Leftrightarrow &-19x & = &4\\\Leftrightarrow & \color{red}{-19}x & = &4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+14}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-13x } & = & 9 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 9 \color{blue}{-14} \\\Leftrightarrow &-25x & = &-5\\\Leftrightarrow & \color{red}{-25}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-5}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-x } & = & 3 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &-12x & = &14\\\Leftrightarrow & \color{red}{-12}x & = &14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+7}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-x } & = & 11 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 11 \color{blue}{-7} \\\Leftrightarrow &-11x & = &4\\\Leftrightarrow & \color{red}{-11}x & = &4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{-14}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-14}\color{blue}{+14-x } & = & -3 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &-16x & = &11\\\Leftrightarrow & \color{red}{-16}x & = &11\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{11}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{16} } & & \\ & V = \left\{ \frac{-11}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+14}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14-x } & = & 5 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{-14} \\\Leftrightarrow &-6x & = &-9\\\Leftrightarrow & \color{red}{-6}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+12}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+12}\color{blue}{-12-13x } & = & 15 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 15 \color{blue}{-12} \\\Leftrightarrow &-19x & = &3\\\Leftrightarrow & \color{red}{-19}x & = &3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{19} } & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{-10}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10-7x } & = & -1 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -1 \color{blue}{+10} \\\Leftrightarrow &3x & = &9\\\Leftrightarrow & \color{red}{3}x & = &9\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{9}{3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)