Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+1}& = & -4 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+1}\color{blue}{-1+13x } & = & -4 \color{red}{ -13x }\color{blue}{-1+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -4 \color{blue}{-1} \\\Leftrightarrow &27x & = &-5\\\Leftrightarrow & \color{red}{27}x & = &-5\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-5}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{27} } & & \\ & V = \left\{ \frac{-5}{27} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+1}& = & 13 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{+1}\color{blue}{-1-3x } & = & 13 \color{red}{ +3x }\color{blue}{-1-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &-x & = &12\\\Leftrightarrow & \color{red}{-}x & = &12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{12}{-1} \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-11}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-11}\color{blue}{+11-x } & = & 7 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &-3x & = &18\\\Leftrightarrow & \color{red}{-3}x & = &18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{18}{-3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-14}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14-x } & = & 6 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 6 \color{blue}{+14} \\\Leftrightarrow &-15x & = &20\\\Leftrightarrow & \color{red}{-15}x & = &20\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{20}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-6}& = & 2 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6+5x } & = & 2 \color{red}{ -5x }\color{blue}{+6+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & 2 \color{blue}{+6} \\\Leftrightarrow &13x & = &8\\\Leftrightarrow & \color{red}{13}x & = &8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-6}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-13x } & = & 1 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 1 \color{blue}{+6} \\\Leftrightarrow &-16x & = &7\\\Leftrightarrow & \color{red}{-16}x & = &7\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{7}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{16} } & & \\ & V = \left\{ \frac{-7}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-2}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-2}\color{blue}{+2-x } & = & -11 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -11 \color{blue}{+2} \\\Leftrightarrow &-9x & = &-9\\\Leftrightarrow & \color{red}{-9}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-9}{-9} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-13}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-13}\color{blue}{+13-13x } & = & -8 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &-25x & = &5\\\Leftrightarrow & \color{red}{-25}x & = &5\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{5}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+11}& = & 4 \color{red}{ +10x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11-10x } & = & 4 \color{red}{ +10x }\color{blue}{-11-10x } \\\Leftrightarrow & 11x \color{blue}{-10x } & = & 4 \color{blue}{-11} \\\Leftrightarrow &x & = &-7\\\Leftrightarrow & \color{red}{}x & = &-7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -7 \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+11}& = & 14 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11+14x } & = & 14 \color{red}{ -14x }\color{blue}{-11+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & 14 \color{blue}{-11} \\\Leftrightarrow &17x & = &3\\\Leftrightarrow & \color{red}{17}x & = &3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+10}& = & 11 \color{red}{ +10x } \\\Leftrightarrow & -13x \color{red}{+10}\color{blue}{-10-10x } & = & 11 \color{red}{ +10x }\color{blue}{-10-10x } \\\Leftrightarrow & -13x \color{blue}{-10x } & = & 11 \color{blue}{-10} \\\Leftrightarrow &-23x & = &1\\\Leftrightarrow & \color{red}{-23}x & = &1\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{1}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{23} } & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+4}& = & 5 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+4}\color{blue}{-4+13x } & = & 5 \color{red}{ -13x }\color{blue}{-4+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 5 \color{blue}{-4} \\\Leftrightarrow &22x & = &1\\\Leftrightarrow & \color{red}{22}x & = &1\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{1}{22} \\\Leftrightarrow & \color{green}{ x = \frac{1}{22} } & & \\ & V = \left\{ \frac{1}{22} \right\} & \\\end{align}\)