Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+4}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-x } & = & 9 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 9 \color{blue}{-4} \\\Leftrightarrow &-5x & = &5\\\Leftrightarrow & \color{red}{-5}x & = &5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{5}{-5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+4}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4-x } & = & 9 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 9 \color{blue}{-4} \\\Leftrightarrow &-16x & = &5\\\Leftrightarrow & \color{red}{-16}x & = &5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{16} } & & \\ & V = \left\{ \frac{-5}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+1}& = & 11 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{+1}\color{blue}{-1-10x } & = & 11 \color{red}{ +10x }\color{blue}{-1-10x } \\\Leftrightarrow & 7x \color{blue}{-10x } & = & 11 \color{blue}{-1} \\\Leftrightarrow &-3x & = &10\\\Leftrightarrow & \color{red}{-3}x & = &10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+11}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+11}\color{blue}{-11-x } & = & -8 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &-4x & = &-19\\\Leftrightarrow & \color{red}{-4}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{19}{4} } & & \\ & V = \left\{ \frac{19}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-1}& = & -13 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1+14x } & = & -13 \color{red}{ -14x }\color{blue}{+1+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & -13 \color{blue}{+1} \\\Leftrightarrow &17x & = &-12\\\Leftrightarrow & \color{red}{17}x & = &-12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{17} } & & \\ & V = \left\{ \frac{-12}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+3}& = & 3 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+3}\color{blue}{-3+14x } & = & 3 \color{red}{ -14x }\color{blue}{-3+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 3 \color{blue}{-3} \\\Leftrightarrow &29x & = &0\\\Leftrightarrow & \color{red}{29}x & = &0\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{0}{29} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-13}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-x } & = & -14 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -14 \color{blue}{+13} \\\Leftrightarrow &-12x & = &-1\\\Leftrightarrow & \color{red}{-12}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-1}& = & -4 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-1}\color{blue}{+1+3x } & = & -4 \color{red}{ -3x }\color{blue}{+1+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -4 \color{blue}{+1} \\\Leftrightarrow &13x & = &-3\\\Leftrightarrow & \color{red}{13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+4}& = & -13 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4-5x } & = & -13 \color{red}{ +5x }\color{blue}{-4-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & -13 \color{blue}{-4} \\\Leftrightarrow &3x & = &-17\\\Leftrightarrow & \color{red}{3}x & = &-17\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-17}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{3} } & & \\ & V = \left\{ \frac{-17}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-15}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15-x } & = & -1 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -1 \color{blue}{+15} \\\Leftrightarrow &7x & = &14\\\Leftrightarrow & \color{red}{7}x & = &14\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{14}{7} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+14}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-x } & = & -6 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -6 \color{blue}{-14} \\\Leftrightarrow &-8x & = &-20\\\Leftrightarrow & \color{red}{-8}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+12}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12-x } & = & 7 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 7 \color{blue}{-12} \\\Leftrightarrow &12x & = &-5\\\Leftrightarrow & \color{red}{12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-5}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)