Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+13}& = & -5 \color{red}{ +10x } \\\Leftrightarrow & -x \color{red}{+13}\color{blue}{-13-10x } & = & -5 \color{red}{ +10x }\color{blue}{-13-10x } \\\Leftrightarrow & -x \color{blue}{-10x } & = & -5 \color{blue}{-13} \\\Leftrightarrow &-11x & = &-18\\\Leftrightarrow & \color{red}{-11}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+13}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+13}\color{blue}{-13-x } & = & -11 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -11 \color{blue}{-13} \\\Leftrightarrow &-4x & = &-24\\\Leftrightarrow & \color{red}{-4}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-24}{-4} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-7}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7-x } & = & -11 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -11 \color{blue}{+7} \\\Leftrightarrow &-16x & = &-4\\\Leftrightarrow & \color{red}{-16}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+13}& = & 7 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+13}\color{blue}{-13+7x } & = & 7 \color{red}{ -7x }\color{blue}{-13+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 7 \color{blue}{-13} \\\Leftrightarrow &19x & = &-6\\\Leftrightarrow & \color{red}{19}x & = &-6\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-6}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{19} } & & \\ & V = \left\{ \frac{-6}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+6}& = & 6 \color{red}{ -6x } \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6+6x } & = & 6 \color{red}{ -6x }\color{blue}{-6+6x } \\\Leftrightarrow & x \color{blue}{+6x } & = & 6 \color{blue}{-6} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-13}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13-7x } & = & 15 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 15 \color{blue}{+13} \\\Leftrightarrow &-20x & = &28\\\Leftrightarrow & \color{red}{-20}x & = &28\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{28}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{-6}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-13x } & = & 11 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 11 \color{blue}{+6} \\\Leftrightarrow &-25x & = &17\\\Leftrightarrow & \color{red}{-25}x & = &17\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{17}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{25} } & & \\ & V = \left\{ \frac{-17}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+12}& = & 10 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12-3x } & = & 10 \color{red}{ +3x }\color{blue}{-12-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &-x & = &-2\\\Leftrightarrow & \color{red}{-}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-2}{-1} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{+1}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+1}\color{blue}{-1-x } & = & 5 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 5 \color{blue}{-1} \\\Leftrightarrow &-3x & = &4\\\Leftrightarrow & \color{red}{-3}x & = &4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-6}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6-x } & = & 13 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 13 \color{blue}{+6} \\\Leftrightarrow &3x & = &19\\\Leftrightarrow & \color{red}{3}x & = &19\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{19}{3} \\\Leftrightarrow & \color{green}{ x = \frac{19}{3} } & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-4}& = & 8 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4-4x } & = & 8 \color{red}{ +4x }\color{blue}{+4-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &-19x & = &12\\\Leftrightarrow & \color{red}{-19}x & = &12\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{12}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{19} } & & \\ & V = \left\{ \frac{-12}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+12}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-x } & = & 14 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 14 \color{blue}{-12} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)