Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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