Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-4}& = & -10 \color{red}{ +12x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4-12x } & = & -10 \color{red}{ +12x }\color{blue}{+4-12x } \\\Leftrightarrow & 13x \color{blue}{-12x } & = & -10 \color{blue}{+4} \\\Leftrightarrow &x & = &-6\\\Leftrightarrow & \color{red}{}x & = &-6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -6 \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+7}& = & -6 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7-5x } & = & -6 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -6 \color{blue}{-7} \\\Leftrightarrow &7x & = &-13\\\Leftrightarrow & \color{red}{7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+3}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3-x } & = & 9 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 9 \color{blue}{-3} \\\Leftrightarrow &-6x & = &6\\\Leftrightarrow & \color{red}{-6}x & = &6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{6}{-6} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-7}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{-7}\color{blue}{+7-13x } & = & 12 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & 12 \color{blue}{+7} \\\Leftrightarrow &-4x & = &19\\\Leftrightarrow & \color{red}{-4}x & = &19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{4} } & & \\ & V = \left\{ \frac{-19}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+4}& = & 1 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4+10x } & = & 1 \color{red}{ -10x }\color{blue}{-4+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & 1 \color{blue}{-4} \\\Leftrightarrow &9x & = &-3\\\Leftrightarrow & \color{red}{9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-3}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-5}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-11x } & = & 3 \color{red}{ +11x }\color{blue}{+5-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 3 \color{blue}{+5} \\\Leftrightarrow &-9x & = &8\\\Leftrightarrow & \color{red}{-9}x & = &8\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{8}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+2}& = & 12 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+2}\color{blue}{-2+13x } & = & 12 \color{red}{ -13x }\color{blue}{-2+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 12 \color{blue}{-2} \\\Leftrightarrow &20x & = &10\\\Leftrightarrow & \color{red}{20}x & = &10\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{10}{20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+1}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1-x } & = & -14 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -14 \color{blue}{-1} \\\Leftrightarrow &-9x & = &-15\\\Leftrightarrow & \color{red}{-9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-13}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13-x } & = & 12 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 12 \color{blue}{+13} \\\Leftrightarrow &-5x & = &25\\\Leftrightarrow & \color{red}{-5}x & = &25\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{25}{-5} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+5}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-x } & = & 15 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 15 \color{blue}{-5} \\\Leftrightarrow &-3x & = &10\\\Leftrightarrow & \color{red}{-3}x & = &10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{-8}& = & 11 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8+10x } & = & 11 \color{red}{ -10x }\color{blue}{+8+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 11 \color{blue}{+8} \\\Leftrightarrow &21x & = &19\\\Leftrightarrow & \color{red}{21}x & = &19\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{19}{21} \\\Leftrightarrow & \color{green}{ x = \frac{19}{21} } & & \\ & V = \left\{ \frac{19}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+6}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+6}\color{blue}{-6-x } & = & 7 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)