Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+3}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+3}\color{blue}{-3-11x } & = & 14 \color{red}{ +11x }\color{blue}{-3-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 14 \color{blue}{-3} \\\Leftrightarrow &-9x & = &11\\\Leftrightarrow & \color{red}{-9}x & = &11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{9} } & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-7}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-7}\color{blue}{+7-x } & = & -5 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -5 \color{blue}{+7} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-2}& = & 3 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2+14x } & = & 3 \color{red}{ -14x }\color{blue}{+2+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 3 \color{blue}{+2} \\\Leftrightarrow &29x & = &5\\\Leftrightarrow & \color{red}{29}x & = &5\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{5}{29} \\\Leftrightarrow & \color{green}{ x = \frac{5}{29} } & & \\ & V = \left\{ \frac{5}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{+3}& = & -6 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3-10x } & = & -6 \color{red}{ +10x }\color{blue}{-3-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -6 \color{blue}{-3} \\\Leftrightarrow &-19x & = &-9\\\Leftrightarrow & \color{red}{-19}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-9}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{9}{19} } & & \\ & V = \left\{ \frac{9}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-6}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-6}\color{blue}{+6-x } & = & 6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 6 \color{blue}{+6} \\\Leftrightarrow &-6x & = &12\\\Leftrightarrow & \color{red}{-6}x & = &12\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{12}{-6} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+10}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10-7x } & = & -7 \color{red}{ +7x }\color{blue}{-10-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -7 \color{blue}{-10} \\\Leftrightarrow &-16x & = &-17\\\Leftrightarrow & \color{red}{-16}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-17}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{17}{16} } & & \\ & V = \left\{ \frac{17}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-13}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13-x } & = & -12 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -12 \color{blue}{+13} \\\Leftrightarrow &-5x & = &1\\\Leftrightarrow & \color{red}{-5}x & = &1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-2}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-2}\color{blue}{+2-x } & = & 14 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 14 \color{blue}{+2} \\\Leftrightarrow &-6x & = &16\\\Leftrightarrow & \color{red}{-6}x & = &16\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{16}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{+7}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+7}\color{blue}{-7-5x } & = & 10 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 10 \color{blue}{-7} \\\Leftrightarrow &-14x & = &3\\\Leftrightarrow & \color{red}{-14}x & = &3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+8}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-7x } & = & -2 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &-17x & = &-10\\\Leftrightarrow & \color{red}{-17}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-12}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12-5x } & = & 3 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & x \color{blue}{-5x } & = & 3 \color{blue}{+12} \\\Leftrightarrow &-4x & = &15\\\Leftrightarrow & \color{red}{-4}x & = &15\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{15}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{4} } & & \\ & V = \left\{ \frac{-15}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-5}& = & 12 \color{red}{ -13x } \\\Leftrightarrow & x \color{red}{-5}\color{blue}{+5+13x } & = & 12 \color{red}{ -13x }\color{blue}{+5+13x } \\\Leftrightarrow & x \color{blue}{+13x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &14x & = &17\\\Leftrightarrow & \color{red}{14}x & = &17\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{17}{14} \\\Leftrightarrow & \color{green}{ x = \frac{17}{14} } & & \\ & V = \left\{ \frac{17}{14} \right\} & \\\end{align}\)