Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+7}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7-11x } & = & -2 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & x \color{blue}{-11x } & = & -2 \color{blue}{-7} \\\Leftrightarrow &-10x & = &-9\\\Leftrightarrow & \color{red}{-10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+5}& = & -8 \color{red}{ +6x } \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5-6x } & = & -8 \color{red}{ +6x }\color{blue}{-5-6x } \\\Leftrightarrow & 7x \color{blue}{-6x } & = & -8 \color{blue}{-5} \\\Leftrightarrow &x & = &-13\\\Leftrightarrow & \color{red}{}x & = &-13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -13 \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-12}& = & 4 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12+8x } & = & 4 \color{red}{ -8x }\color{blue}{+12+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 4 \color{blue}{+12} \\\Leftrightarrow &19x & = &16\\\Leftrightarrow & \color{red}{19}x & = &16\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{16}{19} \\\Leftrightarrow & \color{green}{ x = \frac{16}{19} } & & \\ & V = \left\{ \frac{16}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-15}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-5x } & = & 1 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & -6x \color{blue}{-5x } & = & 1 \color{blue}{+15} \\\Leftrightarrow &-11x & = &16\\\Leftrightarrow & \color{red}{-11}x & = &16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{+6}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+6}\color{blue}{-6-x } & = & -9 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -9 \color{blue}{-6} \\\Leftrightarrow &x & = &-15\\\Leftrightarrow & \color{red}{}x & = &-15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -15 \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-4}& = & 11 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{-4}\color{blue}{+4-3x } & = & 11 \color{red}{ +3x }\color{blue}{+4-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &7x & = &15\\\Leftrightarrow & \color{red}{7}x & = &15\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{15}{7} \\\Leftrightarrow & \color{green}{ x = \frac{15}{7} } & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+13}& = & -13 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13+13x } & = & -13 \color{red}{ -13x }\color{blue}{-13+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & -13 \color{blue}{-13} \\\Leftrightarrow &21x & = &-26\\\Leftrightarrow & \color{red}{21}x & = &-26\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-26}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{21} } & & \\ & V = \left\{ \frac{-26}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-11}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-11}\color{blue}{+11-7x } & = & -9 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & -9 \color{blue}{+11} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+2}& = & -10 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2+7x } & = & -10 \color{red}{ -7x }\color{blue}{-2+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &18x & = &-12\\\Leftrightarrow & \color{red}{18}x & = &-12\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{-12}{18} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+12}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12-11x } & = & 9 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &-9x & = &-3\\\Leftrightarrow & \color{red}{-9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+7}\color{blue}{-7-x } & = & 14 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 14 \color{blue}{-7} \\\Leftrightarrow &-10x & = &7\\\Leftrightarrow & \color{red}{-10}x & = &7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+4}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4-11x } & = & -15 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & -6x \color{blue}{-11x } & = & -15 \color{blue}{-4} \\\Leftrightarrow &-17x & = &-19\\\Leftrightarrow & \color{red}{-17}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-19}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{19}{17} } & & \\ & V = \left\{ \frac{19}{17} \right\} & \\\end{align}\)