Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-11}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11-x } & = & 12 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 12 \color{blue}{+11} \\\Leftrightarrow &x & = &23\\\Leftrightarrow & \color{red}{}x & = &23\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 23 \\\Leftrightarrow & \color{green}{ x = 23 } & & \\ & V = \left\{ 23 \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-9}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9-11x } & = & 10 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &-21x & = &19\\\Leftrightarrow & \color{red}{-21}x & = &19\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{19}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{21} } & & \\ & V = \left\{ \frac{-19}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+11}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+11}\color{blue}{-11-x } & = & 6 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 6 \color{blue}{-11} \\\Leftrightarrow &13x & = &-5\\\Leftrightarrow & \color{red}{13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{-9}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-x } & = & 14 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 14 \color{blue}{+9} \\\Leftrightarrow &-3x & = &23\\\Leftrightarrow & \color{red}{-3}x & = &23\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{23}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{3} } & & \\ & V = \left\{ \frac{-23}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+4}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4-x } & = & 3 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 3 \color{blue}{-4} \\\Leftrightarrow &11x & = &-1\\\Leftrightarrow & \color{red}{11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{+15}& = & -10 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+15}\color{blue}{-15+13x } & = & -10 \color{red}{ -13x }\color{blue}{-15+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -10 \color{blue}{-15} \\\Leftrightarrow &20x & = &-25\\\Leftrightarrow & \color{red}{20}x & = &-25\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-25}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-12}& = & -15 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12-4x } & = & -15 \color{red}{ +4x }\color{blue}{+12-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & -15 \color{blue}{+12} \\\Leftrightarrow &5x & = &-3\\\Leftrightarrow & \color{red}{5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+3}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3-13x } & = & 7 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & 7 \color{blue}{-3} \\\Leftrightarrow &-9x & = &4\\\Leftrightarrow & \color{red}{-9}x & = &4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{+14}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+14}\color{blue}{-14-x } & = & 9 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 9 \color{blue}{-14} \\\Leftrightarrow &-15x & = &-5\\\Leftrightarrow & \color{red}{-15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+8}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+8}\color{blue}{-8-x } & = & -15 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -15 \color{blue}{-8} \\\Leftrightarrow &12x & = &-23\\\Leftrightarrow & \color{red}{12}x & = &-23\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-23}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{12} } & & \\ & V = \left\{ \frac{-23}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-3}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3-x } & = & 8 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 8 \color{blue}{+3} \\\Leftrightarrow &-14x & = &11\\\Leftrightarrow & \color{red}{-14}x & = &11\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{11}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+4}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4-x } & = & -8 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -8 \color{blue}{-4} \\\Leftrightarrow &-15x & = &-12\\\Leftrightarrow & \color{red}{-15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)