Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{+14}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{+14}\color{blue}{-14-x } & = & 3 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 3 \color{blue}{-14} \\\Leftrightarrow &6x & = &-11\\\Leftrightarrow & \color{red}{6}x & = &-11\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-11}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+2}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2-x } & = & -14 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -14 \color{blue}{-2} \\\Leftrightarrow &-12x & = &-16\\\Leftrightarrow & \color{red}{-12}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+6}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+6}\color{blue}{-6-5x } & = & 10 \color{red}{ +5x }\color{blue}{-6-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 10 \color{blue}{-6} \\\Leftrightarrow &-17x & = &4\\\Leftrightarrow & \color{red}{-17}x & = &4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+4}& = & 15 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4+5x } & = & 15 \color{red}{ -5x }\color{blue}{-4+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 15 \color{blue}{-4} \\\Leftrightarrow &11x & = &11\\\Leftrightarrow & \color{red}{11}x & = &11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{11}{11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-9}& = & 14 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9+9x } & = & 14 \color{red}{ -9x }\color{blue}{+9+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 14 \color{blue}{+9} \\\Leftrightarrow &19x & = &23\\\Leftrightarrow & \color{red}{19}x & = &23\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{23}{19} \\\Leftrightarrow & \color{green}{ x = \frac{23}{19} } & & \\ & V = \left\{ \frac{23}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-4}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{-4}\color{blue}{+4-7x } & = & -6 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -6 \color{blue}{+4} \\\Leftrightarrow &-16x & = &-2\\\Leftrightarrow & \color{red}{-16}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{+7}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7-x } & = & 12 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 12 \color{blue}{-7} \\\Leftrightarrow &-12x & = &5\\\Leftrightarrow & \color{red}{-12}x & = &5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-13}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13-x } & = & 3 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 3 \color{blue}{+13} \\\Leftrightarrow &-8x & = &16\\\Leftrightarrow & \color{red}{-8}x & = &16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{16}{-8} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+8}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8-5x } & = & -7 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -7 \color{blue}{-8} \\\Leftrightarrow &x & = &-15\\\Leftrightarrow & \color{red}{}x & = &-15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -15 \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+5}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{+5}\color{blue}{-5-4x } & = & -1 \color{red}{ +4x }\color{blue}{-5-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & -1 \color{blue}{-5} \\\Leftrightarrow &11x & = &-6\\\Leftrightarrow & \color{red}{11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-13}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13-x } & = & -12 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -12 \color{blue}{+13} \\\Leftrightarrow &-4x & = &1\\\Leftrightarrow & \color{red}{-4}x & = &1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-7}& = & -1 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7+7x } & = & -1 \color{red}{ -7x }\color{blue}{+7+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -1 \color{blue}{+7} \\\Leftrightarrow &19x & = &6\\\Leftrightarrow & \color{red}{19}x & = &6\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{6}{19} \\\Leftrightarrow & \color{green}{ x = \frac{6}{19} } & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)