Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-1}& = & 9 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1+13x } & = & 9 \color{red}{ -13x }\color{blue}{+1+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &27x & = &10\\\Leftrightarrow & \color{red}{27}x & = &10\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{10}{27} \\\Leftrightarrow & \color{green}{ x = \frac{10}{27} } & & \\ & V = \left\{ \frac{10}{27} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+1}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+1}\color{blue}{-1-7x } & = & 11 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 11 \color{blue}{-1} \\\Leftrightarrow &3x & = &10\\\Leftrightarrow & \color{red}{3}x & = &10\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{10}{3} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-7}& = & 12 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-7}\color{blue}{+7+14x } & = & 12 \color{red}{ -14x }\color{blue}{+7+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 12 \color{blue}{+7} \\\Leftrightarrow &29x & = &19\\\Leftrightarrow & \color{red}{29}x & = &19\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{19}{29} \\\Leftrightarrow & \color{green}{ x = \frac{19}{29} } & & \\ & V = \left\{ \frac{19}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-4}& = & -6 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{-4}\color{blue}{+4-8x } & = & -6 \color{red}{ +8x }\color{blue}{+4-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & -6 \color{blue}{+4} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-14}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14-x } & = & -12 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -12 \color{blue}{+14} \\\Leftrightarrow &-8x & = &2\\\Leftrightarrow & \color{red}{-8}x & = &2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-11}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-11x } & = & -14 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &-16x & = &-3\\\Leftrightarrow & \color{red}{-16}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{16} } & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+11}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+11}\color{blue}{-11-x } & = & 1 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 1 \color{blue}{-11} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+13}& = & -7 \color{red}{ +12x } \\\Leftrightarrow & -7x \color{red}{+13}\color{blue}{-13-12x } & = & -7 \color{red}{ +12x }\color{blue}{-13-12x } \\\Leftrightarrow & -7x \color{blue}{-12x } & = & -7 \color{blue}{-13} \\\Leftrightarrow &-19x & = &-20\\\Leftrightarrow & \color{red}{-19}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-20}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{20}{19} } & & \\ & V = \left\{ \frac{20}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+1}& = & -13 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{+1}\color{blue}{-1+6x } & = & -13 \color{red}{ -6x }\color{blue}{-1+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & -13 \color{blue}{-1} \\\Leftrightarrow &13x & = &-14\\\Leftrightarrow & \color{red}{13}x & = &-14\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-14}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{13} } & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-7}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7-x } & = & -4 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -4 \color{blue}{+7} \\\Leftrightarrow &-12x & = &3\\\Leftrightarrow & \color{red}{-12}x & = &3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+4}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x } & = & -2 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &-14x & = &-6\\\Leftrightarrow & \color{red}{-14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-10}& = & -4 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10+12x } & = & -4 \color{red}{ -12x }\color{blue}{+10+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & -4 \color{blue}{+10} \\\Leftrightarrow &17x & = &6\\\Leftrightarrow & \color{red}{17}x & = &6\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{6}{17} \\\Leftrightarrow & \color{green}{ x = \frac{6}{17} } & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)