Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-6}& = & 7 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6+8x } & = & 7 \color{red}{ -8x }\color{blue}{+6+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 7 \color{blue}{+6} \\\Leftrightarrow &17x & = &13\\\Leftrightarrow & \color{red}{17}x & = &13\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{13}{17} \\\Leftrightarrow & \color{green}{ x = \frac{13}{17} } & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{+10}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+10}\color{blue}{-10-x } & = & -2 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -2 \color{blue}{-10} \\\Leftrightarrow &-15x & = &-12\\\Leftrightarrow & \color{red}{-15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-10}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10-x } & = & -12 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -12 \color{blue}{+10} \\\Leftrightarrow &x & = &-2\\\Leftrightarrow & \color{red}{}x & = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+8}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8-x } & = & -4 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -4 \color{blue}{-8} \\\Leftrightarrow &-12x & = &-12\\\Leftrightarrow & \color{red}{-12}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-12}{-12} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-4}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4+11x } & = & 4 \color{red}{ -11x }\color{blue}{+4+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & 4 \color{blue}{+4} \\\Leftrightarrow &25x & = &8\\\Leftrightarrow & \color{red}{25}x & = &8\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{8}{25} \\\Leftrightarrow & \color{green}{ x = \frac{8}{25} } & & \\ & V = \left\{ \frac{8}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+13}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+13}\color{blue}{-13-x } & = & -15 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -15 \color{blue}{-13} \\\Leftrightarrow &9x & = &-28\\\Leftrightarrow & \color{red}{9}x & = &-28\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-28}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{9} } & & \\ & V = \left\{ \frac{-28}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-4}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-4}\color{blue}{+4-13x } & = & 7 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 7 \color{blue}{+4} \\\Leftrightarrow &-16x & = &11\\\Leftrightarrow & \color{red}{-16}x & = &11\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{11}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{16} } & & \\ & V = \left\{ \frac{-11}{16} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-7}& = & -14 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-7}\color{blue}{+7-10x } & = & -14 \color{red}{ +10x }\color{blue}{+7-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & -14 \color{blue}{+7} \\\Leftrightarrow &-x & = &-7\\\Leftrightarrow & \color{red}{-}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-7}{-1} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-8}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8-x } & = & -11 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -11 \color{blue}{+8} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+15}& = & -5 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15+6x } & = & -5 \color{red}{ -6x }\color{blue}{-15+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -5 \color{blue}{-15} \\\Leftrightarrow &19x & = &-20\\\Leftrightarrow & \color{red}{19}x & = &-20\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-20}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{19} } & & \\ & V = \left\{ \frac{-20}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+9}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+9}\color{blue}{-9-13x } & = & -3 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -3 \color{blue}{-9} \\\Leftrightarrow &-19x & = &-12\\\Leftrightarrow & \color{red}{-19}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-12}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{12}{19} } & & \\ & V = \left\{ \frac{12}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{-2}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-2}\color{blue}{+2-x } & = & -14 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -14 \color{blue}{+2} \\\Leftrightarrow &-10x & = &-12\\\Leftrightarrow & \color{red}{-10}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-12}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)