Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+12}& = & -3 \color{red}{ +5x } \\\Leftrightarrow & -7x \color{red}{+12}\color{blue}{-12-5x } & = & -3 \color{red}{ +5x }\color{blue}{-12-5x } \\\Leftrightarrow & -7x \color{blue}{-5x } & = & -3 \color{blue}{-12} \\\Leftrightarrow &-12x & = &-15\\\Leftrightarrow & \color{red}{-12}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-15}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{-13}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13-x } & = & -8 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &-8x & = &5\\\Leftrightarrow & \color{red}{-8}x & = &5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{+2}& = & 2 \color{red}{ +8x } \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2-8x } & = & 2 \color{red}{ +8x }\color{blue}{-2-8x } \\\Leftrightarrow & -x \color{blue}{-8x } & = & 2 \color{blue}{-2} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-2}& = & -8 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2+11x } & = & -8 \color{red}{ -11x }\color{blue}{+2+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -8 \color{blue}{+2} \\\Leftrightarrow &26x & = &-6\\\Leftrightarrow & \color{red}{26}x & = &-6\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-6}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-2}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-x } & = & -11 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -11 \color{blue}{+2} \\\Leftrightarrow &-16x & = &-9\\\Leftrightarrow & \color{red}{-16}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-9}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{9}{16} } & & \\ & V = \left\{ \frac{9}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-12}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12-x } & = & -15 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -15 \color{blue}{+12} \\\Leftrightarrow &-10x & = &-3\\\Leftrightarrow & \color{red}{-10}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{10} } & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-11}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{-11}\color{blue}{+11-5x } & = & -7 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & 13x \color{blue}{-5x } & = & -7 \color{blue}{+11} \\\Leftrightarrow &8x & = &4\\\Leftrightarrow & \color{red}{8}x & = &4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-3}& = & 4 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{-3}\color{blue}{+3-5x } & = & 4 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & 4 \color{blue}{+3} \\\Leftrightarrow &-x & = &7\\\Leftrightarrow & \color{red}{-}x & = &7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{7}{-1} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+11}& = & 4 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-4x } & = & 4 \color{red}{ +4x }\color{blue}{-11-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & 4 \color{blue}{-11} \\\Leftrightarrow &-19x & = &-7\\\Leftrightarrow & \color{red}{-19}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-7}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-4}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-4}\color{blue}{+4-11x } & = & -14 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -14 \color{blue}{+4} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+2}& = & 15 \color{red}{ +2x } \\\Leftrightarrow & 15x \color{red}{+2}\color{blue}{-2-2x } & = & 15 \color{red}{ +2x }\color{blue}{-2-2x } \\\Leftrightarrow & 15x \color{blue}{-2x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &13x & = &13\\\Leftrightarrow & \color{red}{13}x & = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{-7}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-x } & = & -5 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -5 \color{blue}{+7} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)