Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-x } & = & 4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 4 \color{blue}{-13} \\\Leftrightarrow &-13x & = &-9\\\Leftrightarrow & \color{red}{-13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{+12}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+12}\color{blue}{-12-x } & = & 11 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-6}& = & 11 \color{red}{ +2x } \\\Leftrightarrow & 11x \color{red}{-6}\color{blue}{+6-2x } & = & 11 \color{red}{ +2x }\color{blue}{+6-2x } \\\Leftrightarrow & 11x \color{blue}{-2x } & = & 11 \color{blue}{+6} \\\Leftrightarrow &9x & = &17\\\Leftrightarrow & \color{red}{9}x & = &17\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{17}{9} \\\Leftrightarrow & \color{green}{ x = \frac{17}{9} } & & \\ & V = \left\{ \frac{17}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+15}& = & -7 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+15}\color{blue}{-15+13x } & = & -7 \color{red}{ -13x }\color{blue}{-15+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -7 \color{blue}{-15} \\\Leftrightarrow &27x & = &-22\\\Leftrightarrow & \color{red}{27}x & = &-22\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-22}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{27} } & & \\ & V = \left\{ \frac{-22}{27} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-13}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13-5x } & = & 7 \color{red}{ +5x }\color{blue}{+13-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &x & = &20\\\Leftrightarrow & \color{red}{}x & = &20\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 20 \\\Leftrightarrow & \color{green}{ x = 20 } & & \\ & V = \left\{ 20 \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+8}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+8}\color{blue}{-8-5x } & = & 14 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 14 \color{blue}{-8} \\\Leftrightarrow &-17x & = &6\\\Leftrightarrow & \color{red}{-17}x & = &6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{17} } & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+2}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2-13x } & = & 8 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 8 \color{blue}{-2} \\\Leftrightarrow &-28x & = &6\\\Leftrightarrow & \color{red}{-28}x & = &6\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{6}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-6}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-6}\color{blue}{+6-x } & = & 9 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 9 \color{blue}{+6} \\\Leftrightarrow &-9x & = &15\\\Leftrightarrow & \color{red}{-9}x & = &15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-4}& = & 2 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4-14x } & = & 2 \color{red}{ +14x }\color{blue}{+4-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & 2 \color{blue}{+4} \\\Leftrightarrow &-x & = &6\\\Leftrightarrow & \color{red}{-}x & = &6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{6}{-1} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+5}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-x } & = & -12 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -12 \color{blue}{-5} \\\Leftrightarrow &-6x & = &-17\\\Leftrightarrow & \color{red}{-6}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{17}{6} } & & \\ & V = \left\{ \frac{17}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-13}& = & 10 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{-13}\color{blue}{+13-9x } & = & 10 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & 7x \color{blue}{-9x } & = & 10 \color{blue}{+13} \\\Leftrightarrow &-2x & = &23\\\Leftrightarrow & \color{red}{-2}x & = &23\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{23}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{2} } & & \\ & V = \left\{ \frac{-23}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+3}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3-x } & = & 11 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 11 \color{blue}{-3} \\\Leftrightarrow &-12x & = &8\\\Leftrightarrow & \color{red}{-12}x & = &8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)