Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+13}& = & -15 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{+13}\color{blue}{-13-8x } & = & -15 \color{red}{ +8x }\color{blue}{-13-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & -15 \color{blue}{-13} \\\Leftrightarrow &-3x & = &-28\\\Leftrightarrow & \color{red}{-3}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-28}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{28}{3} } & & \\ & V = \left\{ \frac{28}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+14}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14-x } & = & -13 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -13 \color{blue}{-14} \\\Leftrightarrow &-7x & = &-27\\\Leftrightarrow & \color{red}{-7}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-27}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{27}{7} } & & \\ & V = \left\{ \frac{27}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{-2}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-2}\color{blue}{+2-x } & = & 6 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 6 \color{blue}{+2} \\\Leftrightarrow &-12x & = &8\\\Leftrightarrow & \color{red}{-12}x & = &8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{+6}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6-9x } & = & -12 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -12 \color{blue}{-6} \\\Leftrightarrow &-17x & = &-18\\\Leftrightarrow & \color{red}{-17}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-18}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{18}{17} } & & \\ & V = \left\{ \frac{18}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-13}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-13}\color{blue}{+13-x } & = & -8 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &-13x & = &5\\\Leftrightarrow & \color{red}{-13}x & = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-14}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14-9x } & = & -12 \color{red}{ +9x }\color{blue}{+14-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & -12 \color{blue}{+14} \\\Leftrightarrow &-20x & = &2\\\Leftrightarrow & \color{red}{-20}x & = &2\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{2}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+11}& = & 1 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+11}\color{blue}{-11+9x } & = & 1 \color{red}{ -9x }\color{blue}{-11+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 1 \color{blue}{-11} \\\Leftrightarrow &19x & = &-10\\\Leftrightarrow & \color{red}{19}x & = &-10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{19} } & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+13}& = & 10 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{+13}\color{blue}{-13-6x } & = & 10 \color{red}{ +6x }\color{blue}{-13-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & 10 \color{blue}{-13} \\\Leftrightarrow &-x & = &-3\\\Leftrightarrow & \color{red}{-}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-3}{-1} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+8}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8-11x } & = & 4 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 4 \color{blue}{-8} \\\Leftrightarrow &-3x & = &-4\\\Leftrightarrow & \color{red}{-3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-4}& = & -3 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4-14x } & = & -3 \color{red}{ +14x }\color{blue}{+4-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & -3 \color{blue}{+4} \\\Leftrightarrow &-x & = &1\\\Leftrightarrow & \color{red}{-}x & = &1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{1}{-1} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-2}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-x } & = & -5 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+11}& = & 8 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{+11}\color{blue}{-11-3x } & = & 8 \color{red}{ +3x }\color{blue}{-11-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & 8 \color{blue}{-11} \\\Leftrightarrow &-17x & = &-3\\\Leftrightarrow & \color{red}{-17}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)