Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-7}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7-13x } & = & 10 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 10 \color{blue}{+7} \\\Leftrightarrow &-16x & = &17\\\Leftrightarrow & \color{red}{-16}x & = &17\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{17}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{16} } & & \\ & V = \left\{ \frac{-17}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+6}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-x } & = & 6 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 6 \color{blue}{-6} \\\Leftrightarrow &-16x & = &0\\\Leftrightarrow & \color{red}{-16}x & = &0\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{0}{-16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+4}& = & -11 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+4}\color{blue}{-4+4x } & = & -11 \color{red}{ -4x }\color{blue}{-4+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -11 \color{blue}{-4} \\\Leftrightarrow &9x & = &-15\\\Leftrightarrow & \color{red}{9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-15}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{-5}& = & 12 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5+11x } & = & 12 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &15x & = &17\\\Leftrightarrow & \color{red}{15}x & = &17\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{17}{15} \\\Leftrightarrow & \color{green}{ x = \frac{17}{15} } & & \\ & V = \left\{ \frac{17}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{-14}& = & 10 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14+11x } & = & 10 \color{red}{ -11x }\color{blue}{+14+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 10 \color{blue}{+14} \\\Leftrightarrow &26x & = &24\\\Leftrightarrow & \color{red}{26}x & = &24\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{24}{26} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-6}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-13x } & = & 8 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 8 \color{blue}{+6} \\\Leftrightarrow &-25x & = &14\\\Leftrightarrow & \color{red}{-25}x & = &14\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{14}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{25} } & & \\ & V = \left\{ \frac{-14}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+9}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{+9}\color{blue}{-9-9x } & = & -13 \color{red}{ +9x }\color{blue}{-9-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & -13 \color{blue}{-9} \\\Leftrightarrow &-x & = &-22\\\Leftrightarrow & \color{red}{-}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-22}{-1} \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-9}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-7x } & = & -9 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -9 \color{blue}{+9} \\\Leftrightarrow &-20x & = &0\\\Leftrightarrow & \color{red}{-20}x & = &0\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{0}{-20} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{+9}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9-11x } & = & 14 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & x \color{blue}{-11x } & = & 14 \color{blue}{-9} \\\Leftrightarrow &-10x & = &5\\\Leftrightarrow & \color{red}{-10}x & = &5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{-11}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-11}\color{blue}{+11-x } & = & -1 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -1 \color{blue}{+11} \\\Leftrightarrow &-3x & = &10\\\Leftrightarrow & \color{red}{-3}x & = &10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{-9}& = & -4 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9-4x } & = & -4 \color{red}{ +4x }\color{blue}{+9-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & -4 \color{blue}{+9} \\\Leftrightarrow &5x & = &5\\\Leftrightarrow & \color{red}{5}x & = &5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{5}{5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{+13}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-x } & = & 11 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 11 \color{blue}{-13} \\\Leftrightarrow &-11x & = &-2\\\Leftrightarrow & \color{red}{-11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)