Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-13}& = & -10 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-13}\color{blue}{+13+11x } & = & -10 \color{red}{ -11x }\color{blue}{+13+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & -10 \color{blue}{+13} \\\Leftrightarrow &20x & = &3\\\Leftrightarrow & \color{red}{20}x & = &3\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{3}{20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{20} } & & \\ & V = \left\{ \frac{3}{20} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-2}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2-x } & = & -5 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &-7x & = &-3\\\Leftrightarrow & \color{red}{-7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{+4}& = & 12 \color{red}{ -4x } \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4+4x } & = & 12 \color{red}{ -4x }\color{blue}{-4+4x } \\\Leftrightarrow & -x \color{blue}{+4x } & = & 12 \color{blue}{-4} \\\Leftrightarrow &3x & = &8\\\Leftrightarrow & \color{red}{3}x & = &8\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{8}{3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{-15}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-x } & = & 5 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 5 \color{blue}{+15} \\\Leftrightarrow &-8x & = &20\\\Leftrightarrow & \color{red}{-8}x & = &20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-11}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11-x } & = & -13 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -13 \color{blue}{+11} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+4}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x } & = & -5 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -5 \color{blue}{-4} \\\Leftrightarrow &-14x & = &-9\\\Leftrightarrow & \color{red}{-14}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+3}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+3}\color{blue}{-3-x } & = & 10 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 10 \color{blue}{-3} \\\Leftrightarrow &-5x & = &7\\\Leftrightarrow & \color{red}{-5}x & = &7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+15}& = & -11 \color{red}{ -9x } \\\Leftrightarrow & x \color{red}{+15}\color{blue}{-15+9x } & = & -11 \color{red}{ -9x }\color{blue}{-15+9x } \\\Leftrightarrow & x \color{blue}{+9x } & = & -11 \color{blue}{-15} \\\Leftrightarrow &10x & = &-26\\\Leftrightarrow & \color{red}{10}x & = &-26\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-26}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{+8}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+8}\color{blue}{-8-x } & = & -8 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -8 \color{blue}{-8} \\\Leftrightarrow &-4x & = &-16\\\Leftrightarrow & \color{red}{-4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-16}{-4} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-14}& = & -1 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14+11x } & = & -1 \color{red}{ -11x }\color{blue}{+14+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -1 \color{blue}{+14} \\\Leftrightarrow &23x & = &13\\\Leftrightarrow & \color{red}{23}x & = &13\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{13}{23} \\\Leftrightarrow & \color{green}{ x = \frac{13}{23} } & & \\ & V = \left\{ \frac{13}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+6}& = & -2 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-8x } & = & -2 \color{red}{ +8x }\color{blue}{-6-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & -2 \color{blue}{-6} \\\Leftrightarrow &-13x & = &-8\\\Leftrightarrow & \color{red}{-13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+13}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-x } & = & -4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -4 \color{blue}{-13} \\\Leftrightarrow &-7x & = &-17\\\Leftrightarrow & \color{red}{-7}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)