Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-5}\color{blue}{+5-x } & = & -9 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -9 \color{blue}{+5} \\\Leftrightarrow &-12x & = &-4\\\Leftrightarrow & \color{red}{-12}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-9}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-7x } & = & -2 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -2 \color{blue}{+9} \\\Leftrightarrow &-16x & = &7\\\Leftrightarrow & \color{red}{-16}x & = &7\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{7}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{16} } & & \\ & V = \left\{ \frac{-7}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-4}& = & -10 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4+4x } & = & -10 \color{red}{ -4x }\color{blue}{+4+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -10 \color{blue}{+4} \\\Leftrightarrow &9x & = &-6\\\Leftrightarrow & \color{red}{9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+10}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+10}\color{blue}{-10-13x } & = & 14 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & 14 \color{blue}{-10} \\\Leftrightarrow &-3x & = &4\\\Leftrightarrow & \color{red}{-3}x & = &4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{-10}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & x \color{red}{-10}\color{blue}{+10-11x } & = & 9 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & x \color{blue}{-11x } & = & 9 \color{blue}{+10} \\\Leftrightarrow &-10x & = &19\\\Leftrightarrow & \color{red}{-10}x & = &19\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{19}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{10} } & & \\ & V = \left\{ \frac{-19}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-13}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-x } & = & -2 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -2 \color{blue}{+13} \\\Leftrightarrow &-11x & = &11\\\Leftrightarrow & \color{red}{-11}x & = &11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{11}{-11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+2}& = & 5 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{+2}\color{blue}{-2-7x } & = & 5 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & 5 \color{blue}{-2} \\\Leftrightarrow &x & = &3\\\Leftrightarrow & \color{red}{}x & = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-3}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3-x } & = & -5 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -5 \color{blue}{+3} \\\Leftrightarrow &-12x & = &-2\\\Leftrightarrow & \color{red}{-12}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+6}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6-x } & = & -14 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -14 \color{blue}{-6} \\\Leftrightarrow &3x & = &-20\\\Leftrightarrow & \color{red}{3}x & = &-20\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-20}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{3} } & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-15}& = & -12 \color{red}{ +12x } \\\Leftrightarrow & 5x \color{red}{-15}\color{blue}{+15-12x } & = & -12 \color{red}{ +12x }\color{blue}{+15-12x } \\\Leftrightarrow & 5x \color{blue}{-12x } & = & -12 \color{blue}{+15} \\\Leftrightarrow &-7x & = &3\\\Leftrightarrow & \color{red}{-7}x & = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+10}& = & -4 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{+10}\color{blue}{-10+14x } & = & -4 \color{red}{ -14x }\color{blue}{-10+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & -4 \color{blue}{-10} \\\Leftrightarrow &17x & = &-14\\\Leftrightarrow & \color{red}{17}x & = &-14\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-14}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{17} } & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-10}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-10}\color{blue}{+10+11x } & = & -7 \color{red}{ -11x }\color{blue}{+10+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &15x & = &3\\\Leftrightarrow & \color{red}{15}x & = &3\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{3}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)