Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+4}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4-11x } & = & 14 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 14 \color{blue}{-4} \\\Leftrightarrow &-9x & = &10\\\Leftrightarrow & \color{red}{-9}x & = &10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-4}& = & 8 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4+6x } & = & 8 \color{red}{ -6x }\color{blue}{+4+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &13x & = &12\\\Leftrightarrow & \color{red}{13}x & = &12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-15}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-x } & = & 4 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 4 \color{blue}{+15} \\\Leftrightarrow &-8x & = &19\\\Leftrightarrow & \color{red}{-8}x & = &19\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{19}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{8} } & & \\ & V = \left\{ \frac{-19}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+2}& = & -12 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+2}\color{blue}{-2+11x } & = & -12 \color{red}{ -11x }\color{blue}{-2+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -12 \color{blue}{-2} \\\Leftrightarrow &23x & = &-14\\\Leftrightarrow & \color{red}{23}x & = &-14\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-14}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{23} } & & \\ & V = \left\{ \frac{-14}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+6}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6-9x } & = & 12 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & 5x \color{blue}{-9x } & = & 12 \color{blue}{-6} \\\Leftrightarrow &-4x & = &6\\\Leftrightarrow & \color{red}{-4}x & = &6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+15}& = & -13 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15-10x } & = & -13 \color{red}{ +10x }\color{blue}{-15-10x } \\\Leftrightarrow & 13x \color{blue}{-10x } & = & -13 \color{blue}{-15} \\\Leftrightarrow &3x & = &-28\\\Leftrightarrow & \color{red}{3}x & = &-28\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-28}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{3} } & & \\ & V = \left\{ \frac{-28}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+14}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+14}\color{blue}{-14-x } & = & 9 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 9 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-5\\\Leftrightarrow & \color{red}{-5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-5}{-5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{+10}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-3x } & = & -11 \color{red}{ +3x }\color{blue}{-10-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & -11 \color{blue}{-10} \\\Leftrightarrow &-8x & = &-21\\\Leftrightarrow & \color{red}{-8}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-21}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{21}{8} } & & \\ & V = \left\{ \frac{21}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+5}& = & -8 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+5}\color{blue}{-5+11x } & = & -8 \color{red}{ -11x }\color{blue}{-5+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -8 \color{blue}{-5} \\\Leftrightarrow &26x & = &-13\\\Leftrightarrow & \color{red}{26}x & = &-13\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-13}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+1}& = & 15 \color{red}{ -11x } \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1+11x } & = & 15 \color{red}{ -11x }\color{blue}{-1+11x } \\\Leftrightarrow & -x \color{blue}{+11x } & = & 15 \color{blue}{-1} \\\Leftrightarrow &10x & = &14\\\Leftrightarrow & \color{red}{10}x & = &14\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{14}{10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-6}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6-x } & = & -15 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -15 \color{blue}{+6} \\\Leftrightarrow &-16x & = &-9\\\Leftrightarrow & \color{red}{-16}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-9}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{9}{16} } & & \\ & V = \left\{ \frac{9}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-3}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3-x } & = & -5 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -5 \color{blue}{+3} \\\Leftrightarrow &-12x & = &-2\\\Leftrightarrow & \color{red}{-12}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)