Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+6}& = & 8 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6+7x } & = & 8 \color{red}{ -7x }\color{blue}{-6+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 8 \color{blue}{-6} \\\Leftrightarrow &15x & = &2\\\Leftrightarrow & \color{red}{15}x & = &2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-3}& = & -13 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{-3}\color{blue}{+3-11x } & = & -13 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & -13 \color{blue}{+3} \\\Leftrightarrow &-13x & = &-10\\\Leftrightarrow & \color{red}{-13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+4}& = & 1 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4+12x } & = & 1 \color{red}{ -12x }\color{blue}{-4+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & 1 \color{blue}{-4} \\\Leftrightarrow &25x & = &-3\\\Leftrightarrow & \color{red}{25}x & = &-3\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-3}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{25} } & & \\ & V = \left\{ \frac{-3}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-11}& = & 3 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11-10x } & = & 3 \color{red}{ +10x }\color{blue}{+11-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &-x & = &14\\\Leftrightarrow & \color{red}{-}x & = &14\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{14}{-1} \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{-2}& = & 10 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2+6x } & = & 10 \color{red}{ -6x }\color{blue}{+2+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & 10 \color{blue}{+2} \\\Leftrightarrow &13x & = &12\\\Leftrightarrow & \color{red}{13}x & = &12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{-14}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14-7x } & = & -8 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & -8 \color{blue}{+14} \\\Leftrightarrow &-3x & = &6\\\Leftrightarrow & \color{red}{-3}x & = &6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{6}{-3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+13}& = & -5 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+13}\color{blue}{-13+9x } & = & -5 \color{red}{ -9x }\color{blue}{-13+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -5 \color{blue}{-13} \\\Leftrightarrow &14x & = &-18\\\Leftrightarrow & \color{red}{14}x & = &-18\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-18}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+3}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-x } & = & -12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -12 \color{blue}{-3} \\\Leftrightarrow &-14x & = &-15\\\Leftrightarrow & \color{red}{-14}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-15}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{15}{14} } & & \\ & V = \left\{ \frac{15}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-2}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2-x } & = & -13 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -13 \color{blue}{+2} \\\Leftrightarrow &-8x & = &-11\\\Leftrightarrow & \color{red}{-8}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{11}{8} } & & \\ & V = \left\{ \frac{11}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+9}& = & -15 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+9}\color{blue}{-9-6x } & = & -15 \color{red}{ +6x }\color{blue}{-9-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &-11x & = &-24\\\Leftrightarrow & \color{red}{-11}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-24}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{24}{11} } & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-12}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-x } & = & 9 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 9 \color{blue}{+12} \\\Leftrightarrow &-6x & = &21\\\Leftrightarrow & \color{red}{-6}x & = &21\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{21}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{-9}& = & 15 \color{red}{ +3x } \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9-3x } & = & 15 \color{red}{ +3x }\color{blue}{+9-3x } \\\Leftrightarrow & 7x \color{blue}{-3x } & = & 15 \color{blue}{+9} \\\Leftrightarrow &4x & = &24\\\Leftrightarrow & \color{red}{4}x & = &24\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{24}{4} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)