Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-9}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-x } & = & -11 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -11 \color{blue}{+9} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-13}& = & 15 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13+13x } & = & 15 \color{red}{ -13x }\color{blue}{+13+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 15 \color{blue}{+13} \\\Leftrightarrow &27x & = &28\\\Leftrightarrow & \color{red}{27}x & = &28\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{28}{27} \\\Leftrightarrow & \color{green}{ x = \frac{28}{27} } & & \\ & V = \left\{ \frac{28}{27} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+11}& = & 3 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11+7x } & = & 3 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 3 \color{blue}{-11} \\\Leftrightarrow &15x & = &-8\\\Leftrightarrow & \color{red}{15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-8}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{-6}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-7x } & = & -4 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & -4 \color{blue}{+6} \\\Leftrightarrow &-10x & = &2\\\Leftrightarrow & \color{red}{-10}x & = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+2}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-x } & = & -9 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -9 \color{blue}{-2} \\\Leftrightarrow &-4x & = &-11\\\Leftrightarrow & \color{red}{-4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-11}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+4}& = & -12 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+4}\color{blue}{-4+9x } & = & -12 \color{red}{ -9x }\color{blue}{-4+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -12 \color{blue}{-4} \\\Leftrightarrow &14x & = &-16\\\Leftrightarrow & \color{red}{14}x & = &-16\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-16}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+12}& = & -3 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{+12}\color{blue}{-12-4x } & = & -3 \color{red}{ +4x }\color{blue}{-12-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & -3 \color{blue}{-12} \\\Leftrightarrow &5x & = &-15\\\Leftrightarrow & \color{red}{5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-15}{5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+13}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+13}\color{blue}{-13-x } & = & -15 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -15 \color{blue}{-13} \\\Leftrightarrow &-15x & = &-28\\\Leftrightarrow & \color{red}{-15}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-28}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{28}{15} } & & \\ & V = \left\{ \frac{28}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{-13}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-13}\color{blue}{+13-5x } & = & 14 \color{red}{ +5x }\color{blue}{+13-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 14 \color{blue}{+13} \\\Leftrightarrow &-17x & = &27\\\Leftrightarrow & \color{red}{-17}x & = &27\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{27}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{17} } & & \\ & V = \left\{ \frac{-27}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-2}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-2}\color{blue}{+2-7x } & = & 14 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & 14 \color{blue}{+2} \\\Leftrightarrow &5x & = &16\\\Leftrightarrow & \color{red}{5}x & = &16\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{16}{5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+5}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+5}\color{blue}{-5-x } & = & -12 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -12 \color{blue}{-5} \\\Leftrightarrow &-7x & = &-17\\\Leftrightarrow & \color{red}{-7}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-1}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1-x } & = & -1 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -1 \color{blue}{+1} \\\Leftrightarrow &-16x & = &0\\\Leftrightarrow & \color{red}{-16}x & = &0\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{0}{-16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)