Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{-12}& = & -8 \color{red}{ +4x } \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12-4x } & = & -8 \color{red}{ +4x }\color{blue}{+12-4x } \\\Leftrightarrow & x \color{blue}{-4x } & = & -8 \color{blue}{+12} \\\Leftrightarrow &-3x & = &4\\\Leftrightarrow & \color{red}{-3}x & = &4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+6}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6-x } & = & -11 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -11 \color{blue}{-6} \\\Leftrightarrow &-3x & = &-17\\\Leftrightarrow & \color{red}{-3}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-17}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{17}{3} } & & \\ & V = \left\{ \frac{17}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-1}& = & -12 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-1}\color{blue}{+1+14x } & = & -12 \color{red}{ -14x }\color{blue}{+1+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -12 \color{blue}{+1} \\\Leftrightarrow &19x & = &-11\\\Leftrightarrow & \color{red}{19}x & = &-11\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-11}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{19} } & & \\ & V = \left\{ \frac{-11}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-10}& = & 8 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10+13x } & = & 8 \color{red}{ -13x }\color{blue}{+10+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 8 \color{blue}{+10} \\\Leftrightarrow &23x & = &18\\\Leftrightarrow & \color{red}{23}x & = &18\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{18}{23} \\\Leftrightarrow & \color{green}{ x = \frac{18}{23} } & & \\ & V = \left\{ \frac{18}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-4}& = & -2 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4-9x } & = & -2 \color{red}{ +9x }\color{blue}{+4-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -2 \color{blue}{+4} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+12}& = & 13 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+12}\color{blue}{-12-11x } & = & 13 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 13 \color{blue}{-12} \\\Leftrightarrow &-21x & = &1\\\Leftrightarrow & \color{red}{-21}x & = &1\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{1}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{21} } & & \\ & V = \left\{ \frac{-1}{21} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{-6}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-x } & = & -5 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -5 \color{blue}{+6} \\\Leftrightarrow &-8x & = &1\\\Leftrightarrow & \color{red}{-8}x & = &1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+13}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+13}\color{blue}{-13-x } & = & -15 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -15 \color{blue}{-13} \\\Leftrightarrow &-15x & = &-28\\\Leftrightarrow & \color{red}{-15}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-28}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{28}{15} } & & \\ & V = \left\{ \frac{28}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+15}& = & -7 \color{red}{ +2x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15-2x } & = & -7 \color{red}{ +2x }\color{blue}{-15-2x } \\\Leftrightarrow & 13x \color{blue}{-2x } & = & -7 \color{blue}{-15} \\\Leftrightarrow &11x & = &-22\\\Leftrightarrow & \color{red}{11}x & = &-22\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-22}{11} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-6}& = & -12 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6+11x } & = & -12 \color{red}{ -11x }\color{blue}{+6+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -12 \color{blue}{+6} \\\Leftrightarrow &15x & = &-6\\\Leftrightarrow & \color{red}{15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-6}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{-8}& = & 14 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8+2x } & = & 14 \color{red}{ -2x }\color{blue}{+8+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 14 \color{blue}{+8} \\\Leftrightarrow &13x & = &22\\\Leftrightarrow & \color{red}{13}x & = &22\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{22}{13} \\\Leftrightarrow & \color{green}{ x = \frac{22}{13} } & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+1}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1-x } & = & 13 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &-10x & = &12\\\Leftrightarrow & \color{red}{-10}x & = &12\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{12}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)