Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+6}& = & 2 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+6}\color{blue}{-6-8x } & = & 2 \color{red}{ +8x }\color{blue}{-6-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 2 \color{blue}{-6} \\\Leftrightarrow &-15x & = &-4\\\Leftrightarrow & \color{red}{-15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-6}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-5x } & = & -8 \color{red}{ +5x }\color{blue}{+6-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -8 \color{blue}{+6} \\\Leftrightarrow &-9x & = &-2\\\Leftrightarrow & \color{red}{-9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+13}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13-x } & = & 14 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & 14 \color{blue}{-13} \\\Leftrightarrow &14x & = &1\\\Leftrightarrow & \color{red}{14}x & = &1\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{1}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-5}& = & 7 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-5}\color{blue}{+5+13x } & = & 7 \color{red}{ -13x }\color{blue}{+5+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 7 \color{blue}{+5} \\\Leftrightarrow &20x & = &12\\\Leftrightarrow & \color{red}{20}x & = &12\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{12}{20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-8}& = & -6 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{-8}\color{blue}{+8-4x } & = & -6 \color{red}{ +4x }\color{blue}{+8-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & -6 \color{blue}{+8} \\\Leftrightarrow &-x & = &2\\\Leftrightarrow & \color{red}{-}x & = &2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{2}{-1} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+2}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-x } & = & 6 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 6 \color{blue}{-2} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-4}& = & 2 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4+6x } & = & 2 \color{red}{ -6x }\color{blue}{+4+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 2 \color{blue}{+4} \\\Leftrightarrow &19x & = &6\\\Leftrightarrow & \color{red}{19}x & = &6\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{6}{19} \\\Leftrightarrow & \color{green}{ x = \frac{6}{19} } & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+14}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14-x } & = & 6 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 6 \color{blue}{-14} \\\Leftrightarrow &5x & = &-8\\\Leftrightarrow & \color{red}{5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{+5}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-x } & = & -5 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -5 \color{blue}{-5} \\\Leftrightarrow &-15x & = &-10\\\Leftrightarrow & \color{red}{-15}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+7}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7-x } & = & -13 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -13 \color{blue}{-7} \\\Leftrightarrow &-6x & = &-20\\\Leftrightarrow & \color{red}{-6}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-20}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2-x } & = & -3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &-10x & = &-5\\\Leftrightarrow & \color{red}{-10}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-5}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5-x } & = & -7 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -7 \color{blue}{+5} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)