Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-3}& = & -10 \color{red}{ +11x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3-11x } & = & -10 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & 13x \color{blue}{-11x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &2x & = &-7\\\Leftrightarrow & \color{red}{2}x & = &-7\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-7}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+6}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6-7x } & = & 1 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & 1 \color{blue}{-6} \\\Leftrightarrow &-9x & = &-5\\\Leftrightarrow & \color{red}{-9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6-x } & = & -3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -3 \color{blue}{+6} \\\Leftrightarrow &11x & = &3\\\Leftrightarrow & \color{red}{11}x & = &3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-10}& = & 15 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10-14x } & = & 15 \color{red}{ +14x }\color{blue}{+10-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 15 \color{blue}{+10} \\\Leftrightarrow &-27x & = &25\\\Leftrightarrow & \color{red}{-27}x & = &25\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{25}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{27} } & & \\ & V = \left\{ \frac{-25}{27} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{-10}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-10}\color{blue}{+10-x } & = & -8 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -8 \color{blue}{+10} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11-x } & = & 3 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &-16x & = &14\\\Leftrightarrow & \color{red}{-16}x & = &14\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{14}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{-5}& = & -8 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5-4x } & = & -8 \color{red}{ +4x }\color{blue}{+5-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -8 \color{blue}{+5} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{-4}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{-4}\color{blue}{+4-5x } & = & 14 \color{red}{ +5x }\color{blue}{+4-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & 14 \color{blue}{+4} \\\Leftrightarrow &-3x & = &18\\\Leftrightarrow & \color{red}{-3}x & = &18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{18}{-3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+11}& = & -1 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11-6x } & = & -1 \color{red}{ +6x }\color{blue}{-11-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &-x & = &-12\\\Leftrightarrow & \color{red}{-}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-12}{-1} \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+8}& = & -3 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8+4x } & = & -3 \color{red}{ -4x }\color{blue}{-8+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -3 \color{blue}{-8} \\\Leftrightarrow &9x & = &-11\\\Leftrightarrow & \color{red}{9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-11}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{9} } & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{+14}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-x } & = & -4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &-13x & = &-18\\\Leftrightarrow & \color{red}{-13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-18}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-6}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-6}\color{blue}{+6-x } & = & -5 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -5 \color{blue}{+6} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)