Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+1}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+1}\color{blue}{-1+13x } & = & -3 \color{red}{ -13x }\color{blue}{-1+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -3 \color{blue}{-1} \\\Leftrightarrow &27x & = &-4\\\Leftrightarrow & \color{red}{27}x & = &-4\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-4}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{27} } & & \\ & V = \left\{ \frac{-4}{27} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+6}& = & -13 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+6}\color{blue}{-6+13x } & = & -13 \color{red}{ -13x }\color{blue}{-6+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -13 \color{blue}{-6} \\\Leftrightarrow &27x & = &-19\\\Leftrightarrow & \color{red}{27}x & = &-19\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-19}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{27} } & & \\ & V = \left\{ \frac{-19}{27} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+3}& = & 4 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3+4x } & = & 4 \color{red}{ -4x }\color{blue}{-3+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 4 \color{blue}{-3} \\\Leftrightarrow &9x & = &1\\\Leftrightarrow & \color{red}{9}x & = &1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{+7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+7}\color{blue}{-7-x } & = & 14 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 14 \color{blue}{-7} \\\Leftrightarrow &-16x & = &7\\\Leftrightarrow & \color{red}{-16}x & = &7\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{7}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{16} } & & \\ & V = \left\{ \frac{-7}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-14}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14-x } & = & 9 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 9 \color{blue}{+14} \\\Leftrightarrow &-14x & = &23\\\Leftrightarrow & \color{red}{-14}x & = &23\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{23}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{14} } & & \\ & V = \left\{ \frac{-23}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+9}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-x } & = & -15 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &-14x & = &-24\\\Leftrightarrow & \color{red}{-14}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-24}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{+3}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+3}\color{blue}{-3-9x } & = & 8 \color{red}{ +9x }\color{blue}{-3-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 8 \color{blue}{-3} \\\Leftrightarrow &-17x & = &5\\\Leftrightarrow & \color{red}{-17}x & = &5\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{5}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{17} } & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+13}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-x } & = & 12 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 12 \color{blue}{-13} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+14}& = & 12 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14+13x } & = & 12 \color{red}{ -13x }\color{blue}{-14+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 12 \color{blue}{-14} \\\Leftrightarrow &24x & = &-2\\\Leftrightarrow & \color{red}{24}x & = &-2\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-2}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-x } & = & 4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 4 \color{blue}{-13} \\\Leftrightarrow &-6x & = &-9\\\Leftrightarrow & \color{red}{-6}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+4}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-11x } & = & 4 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 4 \color{blue}{-4} \\\Leftrightarrow &-21x & = &0\\\Leftrightarrow & \color{red}{-21}x & = &0\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{0}{-21} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-9}& = & -4 \color{red}{ +6x } \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9-6x } & = & -4 \color{red}{ +6x }\color{blue}{+9-6x } \\\Leftrightarrow & 11x \color{blue}{-6x } & = & -4 \color{blue}{+9} \\\Leftrightarrow &5x & = &5\\\Leftrightarrow & \color{red}{5}x & = &5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{5}{5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)