Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+14}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-x } & = & 5 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 5 \color{blue}{-14} \\\Leftrightarrow &-13x & = &-9\\\Leftrightarrow & \color{red}{-13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-7}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7-13x } & = & 3 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 3 \color{blue}{+7} \\\Leftrightarrow &-19x & = &10\\\Leftrightarrow & \color{red}{-19}x & = &10\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{10}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{19} } & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+8}& = & 3 \color{red}{ -15x } \\\Leftrightarrow & x \color{red}{+8}\color{blue}{-8+15x } & = & 3 \color{red}{ -15x }\color{blue}{-8+15x } \\\Leftrightarrow & x \color{blue}{+15x } & = & 3 \color{blue}{-8} \\\Leftrightarrow &16x & = &-5\\\Leftrightarrow & \color{red}{16}x & = &-5\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-5}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{16} } & & \\ & V = \left\{ \frac{-5}{16} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-9}& = & 1 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-6x } & = & 1 \color{red}{ +6x }\color{blue}{+9-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 1 \color{blue}{+9} \\\Leftrightarrow &-11x & = &10\\\Leftrightarrow & \color{red}{-11}x & = &10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{-9}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9-x } & = & 7 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 7 \color{blue}{+9} \\\Leftrightarrow &-7x & = &16\\\Leftrightarrow & \color{red}{-7}x & = &16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{7} } & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-13}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13-x } & = & -9 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -9 \color{blue}{+13} \\\Leftrightarrow &-8x & = &4\\\Leftrightarrow & \color{red}{-8}x & = &4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-9}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9-3x } & = & -11 \color{red}{ +3x }\color{blue}{+9-3x } \\\Leftrightarrow & -x \color{blue}{-3x } & = & -11 \color{blue}{+9} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-10}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10-x } & = & 4 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & 4 \color{blue}{+10} \\\Leftrightarrow &10x & = &14\\\Leftrightarrow & \color{red}{10}x & = &14\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{14}{10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+8}& = & 1 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+8}\color{blue}{-8-11x } & = & 1 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 1 \color{blue}{-8} \\\Leftrightarrow &x & = &-7\\\Leftrightarrow & \color{red}{}x & = &-7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -7 \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+15}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-x } & = & -12 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -12 \color{blue}{-15} \\\Leftrightarrow &-10x & = &-27\\\Leftrightarrow & \color{red}{-10}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-27}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{27}{10} } & & \\ & V = \left\{ \frac{27}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-4}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x } & = & -7 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -7 \color{blue}{+4} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-5}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5-x } & = & 3 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 3 \color{blue}{+5} \\\Leftrightarrow &-13x & = &8\\\Leftrightarrow & \color{red}{-13}x & = &8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)