Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+11}& = & 7 \color{red}{ -8x } \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11+8x } & = & 7 \color{red}{ -8x }\color{blue}{-11+8x } \\\Leftrightarrow & -x \color{blue}{+8x } & = & 7 \color{blue}{-11} \\\Leftrightarrow &7x & = &-4\\\Leftrightarrow & \color{red}{7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-10}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-x } & = & -6 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -6 \color{blue}{+10} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-14}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14-x } & = & -3 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &-9x & = &11\\\Leftrightarrow & \color{red}{-9}x & = &11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{9} } & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+3}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+3}\color{blue}{-3-5x } & = & -7 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -7 \color{blue}{-3} \\\Leftrightarrow &7x & = &-10\\\Leftrightarrow & \color{red}{7}x & = &-10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+14}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14-x } & = & 7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 7 \color{blue}{-14} \\\Leftrightarrow &-4x & = &-7\\\Leftrightarrow & \color{red}{-4}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-12}& = & -14 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12+11x } & = & -14 \color{red}{ -11x }\color{blue}{+12+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -14 \color{blue}{+12} \\\Leftrightarrow &17x & = &-2\\\Leftrightarrow & \color{red}{17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-2}& = & -14 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2+6x } & = & -14 \color{red}{ -6x }\color{blue}{+2+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -14 \color{blue}{+2} \\\Leftrightarrow &19x & = &-12\\\Leftrightarrow & \color{red}{19}x & = &-12\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-12}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{19} } & & \\ & V = \left\{ \frac{-12}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{+13}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13+13x } & = & -3 \color{red}{ -13x }\color{blue}{-13+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -3 \color{blue}{-13} \\\Leftrightarrow &24x & = &-16\\\Leftrightarrow & \color{red}{24}x & = &-16\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-16}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{+7}& = & 9 \color{red}{ -13x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7+13x } & = & 9 \color{red}{ -13x }\color{blue}{-7+13x } \\\Leftrightarrow & x \color{blue}{+13x } & = & 9 \color{blue}{-7} \\\Leftrightarrow &14x & = &2\\\Leftrightarrow & \color{red}{14}x & = &2\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{2}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+12}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+12}\color{blue}{-12-x } & = & -12 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -12 \color{blue}{-12} \\\Leftrightarrow &-16x & = &-24\\\Leftrightarrow & \color{red}{-16}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-24}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{-14}& = & 5 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14+7x } & = & 5 \color{red}{ -7x }\color{blue}{+14+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 5 \color{blue}{+14} \\\Leftrightarrow &19x & = &19\\\Leftrightarrow & \color{red}{19}x & = &19\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{19}{19} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+2}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-13x } & = & 14 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & 14 \color{blue}{-2} \\\Leftrightarrow &-11x & = &12\\\Leftrightarrow & \color{red}{-11}x & = &12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{11} } & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)