Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+13}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+13}\color{blue}{-13-7x } & = & 1 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 1 \color{blue}{-13} \\\Leftrightarrow &3x & = &-12\\\Leftrightarrow & \color{red}{3}x & = &-12\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-12}{3} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+7}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+7}\color{blue}{-7-x } & = & -7 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -7 \color{blue}{-7} \\\Leftrightarrow &-10x & = &-14\\\Leftrightarrow & \color{red}{-10}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-2}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2-x } & = & -2 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -2 \color{blue}{+2} \\\Leftrightarrow &13x & = &0\\\Leftrightarrow & \color{red}{13}x & = &0\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{0}{13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-11}& = & 8 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-3x } & = & 8 \color{red}{ +3x }\color{blue}{+11-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 8 \color{blue}{+11} \\\Leftrightarrow &-8x & = &19\\\Leftrightarrow & \color{red}{-8}x & = &19\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{19}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{8} } & & \\ & V = \left\{ \frac{-19}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{+14}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+14}\color{blue}{-14-x } & = & 9 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 9 \color{blue}{-14} \\\Leftrightarrow &-12x & = &-5\\\Leftrightarrow & \color{red}{-12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-11}& = & -4 \color{red}{ -3x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11+3x } & = & -4 \color{red}{ -3x }\color{blue}{+11+3x } \\\Leftrightarrow & -x \color{blue}{+3x } & = & -4 \color{blue}{+11} \\\Leftrightarrow &2x & = &7\\\Leftrightarrow & \color{red}{2}x & = &7\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{7}{2} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+14}& = & 11 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+14}\color{blue}{-14-9x } & = & 11 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 11 \color{blue}{-14} \\\Leftrightarrow &-13x & = &-3\\\Leftrightarrow & \color{red}{-13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+4}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4-x } & = & -12 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & -12 \color{blue}{-4} \\\Leftrightarrow &6x & = &-16\\\Leftrightarrow & \color{red}{6}x & = &-16\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-16}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-6}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6+13x } & = & 1 \color{red}{ -13x }\color{blue}{+6+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 1 \color{blue}{+6} \\\Leftrightarrow &20x & = &7\\\Leftrightarrow & \color{red}{20}x & = &7\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{7}{20} \\\Leftrightarrow & \color{green}{ x = \frac{7}{20} } & & \\ & V = \left\{ \frac{7}{20} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-9}& = & 11 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9-11x } & = & 11 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & 11 \color{blue}{+9} \\\Leftrightarrow &-7x & = &20\\\Leftrightarrow & \color{red}{-7}x & = &20\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{20}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{7} } & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+8}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-x } & = & 10 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 10 \color{blue}{-8} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-7}& = & -4 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-7}\color{blue}{+7+11x } & = & -4 \color{red}{ -11x }\color{blue}{+7+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & -4 \color{blue}{+7} \\\Leftrightarrow &20x & = &3\\\Leftrightarrow & \color{red}{20}x & = &3\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{3}{20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{20} } & & \\ & V = \left\{ \frac{3}{20} \right\} & \\\end{align}\)