Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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