Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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