Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-7}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-11x } & = & 7 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & 7 \color{blue}{+7} \\\Leftrightarrow &-13x & = &14\\\Leftrightarrow & \color{red}{-13}x & = &14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{13} } & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+13}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+13}\color{blue}{-13-x } & = & -2 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -2 \color{blue}{-13} \\\Leftrightarrow &-16x & = &-15\\\Leftrightarrow & \color{red}{-16}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-15}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{15}{16} } & & \\ & V = \left\{ \frac{15}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+11}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-x } & = & 2 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{-7}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-x } & = & 4 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 4 \color{blue}{+7} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+5}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{+5}\color{blue}{-5-13x } & = & -1 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & -1 \color{blue}{-5} \\\Leftrightarrow &2x & = &-6\\\Leftrightarrow & \color{red}{2}x & = &-6\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-6}{2} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+8}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8-7x } & = & -7 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -7 \color{blue}{-8} \\\Leftrightarrow &3x & = &-15\\\Leftrightarrow & \color{red}{3}x & = &-15\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-15}{3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+15}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-7x } & = & -5 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -5 \color{blue}{-15} \\\Leftrightarrow &-16x & = &-20\\\Leftrightarrow & \color{red}{-16}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-20}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-13}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-x } & = & 11 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 11 \color{blue}{+13} \\\Leftrightarrow &-7x & = &24\\\Leftrightarrow & \color{red}{-7}x & = &24\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{24}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{7} } & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+11}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11-x } & = & -14 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &10x & = &-25\\\Leftrightarrow & \color{red}{10}x & = &-25\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-25}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-11}& = & -1 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11-9x } & = & -1 \color{red}{ +9x }\color{blue}{+11-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & -1 \color{blue}{+11} \\\Leftrightarrow &-7x & = &10\\\Leftrightarrow & \color{red}{-7}x & = &10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-12}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12-11x } & = & 4 \color{red}{ +11x }\color{blue}{+12-11x } \\\Leftrightarrow & -13x \color{blue}{-11x } & = & 4 \color{blue}{+12} \\\Leftrightarrow &-24x & = &16\\\Leftrightarrow & \color{red}{-24}x & = &16\\\Leftrightarrow & \frac{\color{red}{-24}x}{ \color{blue}{ -24}} & = & \frac{16}{-24} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-8}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-x } & = & -13 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &-14x & = &-5\\\Leftrightarrow & \color{red}{-14}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)