Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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