Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-8}& = & 5 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8-3x } & = & 5 \color{red}{ +3x }\color{blue}{+8-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 5 \color{blue}{+8} \\\Leftrightarrow &-8x & = &13\\\Leftrightarrow & \color{red}{-8}x & = &13\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{13}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{8} } & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{+5}& = & -3 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5+6x } & = & -3 \color{red}{ -6x }\color{blue}{-5+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &19x & = &-8\\\Leftrightarrow & \color{red}{19}x & = &-8\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-8}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{19} } & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+9}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-x } & = & 1 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 1 \color{blue}{-9} \\\Leftrightarrow &-11x & = &-8\\\Leftrightarrow & \color{red}{-11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+8}& = & 8 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+8}\color{blue}{-8-11x } & = & 8 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 8 \color{blue}{-8} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+6}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6-x } & = & 9 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 9 \color{blue}{-6} \\\Leftrightarrow &6x & = &3\\\Leftrightarrow & \color{red}{6}x & = &3\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{3}{6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+14}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14-x } & = & -8 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -8 \color{blue}{-14} \\\Leftrightarrow &-3x & = &-22\\\Leftrightarrow & \color{red}{-3}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-22}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{22}{3} } & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+15}& = & -5 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+15}\color{blue}{-15+11x } & = & -5 \color{red}{ -11x }\color{blue}{-15+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -5 \color{blue}{-15} \\\Leftrightarrow &23x & = &-20\\\Leftrightarrow & \color{red}{23}x & = &-20\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-20}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{23} } & & \\ & V = \left\{ \frac{-20}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-15}& = & 10 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-14x } & = & 10 \color{red}{ +14x }\color{blue}{+15-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 10 \color{blue}{+15} \\\Leftrightarrow &-27x & = &25\\\Leftrightarrow & \color{red}{-27}x & = &25\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{25}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{27} } & & \\ & V = \left\{ \frac{-25}{27} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+1}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1+13x } & = & -3 \color{red}{ -13x }\color{blue}{-1+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & -3 \color{blue}{-1} \\\Leftrightarrow &21x & = &-4\\\Leftrightarrow & \color{red}{21}x & = &-4\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-4}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{21} } & & \\ & V = \left\{ \frac{-4}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-13}& = & -13 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13+13x } & = & -13 \color{red}{ -13x }\color{blue}{+13+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -13 \color{blue}{+13} \\\Leftrightarrow &27x & = &0\\\Leftrightarrow & \color{red}{27}x & = &0\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{0}{27} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-7}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7-x } & = & 13 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 13 \color{blue}{+7} \\\Leftrightarrow &-4x & = &20\\\Leftrightarrow & \color{red}{-4}x & = &20\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{20}{-4} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+15}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15-x } & = & 12 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 12 \color{blue}{-15} \\\Leftrightarrow &-14x & = &-3\\\Leftrightarrow & \color{red}{-14}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)