Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-9}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-9}\color{blue}{+9-x } & = & -10 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &-16x & = &-1\\\Leftrightarrow & \color{red}{-16}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+3}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+3}\color{blue}{-3-x } & = & -14 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -14 \color{blue}{-3} \\\Leftrightarrow &11x & = &-17\\\Leftrightarrow & \color{red}{11}x & = &-17\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-17}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-12}& = & 3 \color{red}{ +12x } \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12-12x } & = & 3 \color{red}{ +12x }\color{blue}{+12-12x } \\\Leftrightarrow & 5x \color{blue}{-12x } & = & 3 \color{blue}{+12} \\\Leftrightarrow &-7x & = &15\\\Leftrightarrow & \color{red}{-7}x & = &15\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{15}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+14}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14-x } & = & -12 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -12 \color{blue}{-14} \\\Leftrightarrow &-11x & = &-26\\\Leftrightarrow & \color{red}{-11}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-26}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{26}{11} } & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+1}& = & 2 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1+5x } & = & 2 \color{red}{ -5x }\color{blue}{-1+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 2 \color{blue}{-1} \\\Leftrightarrow &11x & = &1\\\Leftrightarrow & \color{red}{11}x & = &1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+14}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+14}\color{blue}{-14-x } & = & -5 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -5 \color{blue}{-14} \\\Leftrightarrow &-16x & = &-19\\\Leftrightarrow & \color{red}{-16}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-19}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{19}{16} } & & \\ & V = \left\{ \frac{19}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+4}& = & 4 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4+13x } & = & 4 \color{red}{ -13x }\color{blue}{-4+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & 4 \color{blue}{-4} \\\Leftrightarrow &21x & = &0\\\Leftrightarrow & \color{red}{21}x & = &0\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{0}{21} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{+1}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+1}\color{blue}{-1-x } & = & -8 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -8 \color{blue}{-1} \\\Leftrightarrow &-6x & = &-9\\\Leftrightarrow & \color{red}{-6}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{+8}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8-7x } & = & -8 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & -8 \color{blue}{-8} \\\Leftrightarrow &-4x & = &-16\\\Leftrightarrow & \color{red}{-4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-16}{-4} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+14}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-5x } & = & 15 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & -7x \color{blue}{-5x } & = & 15 \color{blue}{-14} \\\Leftrightarrow &-12x & = &1\\\Leftrightarrow & \color{red}{-12}x & = &1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-5}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-5}\color{blue}{+5-13x } & = & 4 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & 4 \color{blue}{+5} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-9}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-11x } & = & 5 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & -13x \color{blue}{-11x } & = & 5 \color{blue}{+9} \\\Leftrightarrow &-24x & = &14\\\Leftrightarrow & \color{red}{-24}x & = &14\\\Leftrightarrow & \frac{\color{red}{-24}x}{ \color{blue}{ -24}} & = & \frac{14}{-24} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{12} } & & \\ & V = \left\{ \frac{-7}{12} \right\} & \\\end{align}\)