Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+12}& = & 15 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12+12x } & = & 15 \color{red}{ -12x }\color{blue}{-12+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & 15 \color{blue}{-12} \\\Leftrightarrow &17x & = &3\\\Leftrightarrow & \color{red}{17}x & = &3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+4}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+4}\color{blue}{-4-x } & = & 6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 6 \color{blue}{-4} \\\Leftrightarrow &9x & = &2\\\Leftrightarrow & \color{red}{9}x & = &2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+3}& = & 10 \color{red}{ +2x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3-2x } & = & 10 \color{red}{ +2x }\color{blue}{-3-2x } \\\Leftrightarrow & 9x \color{blue}{-2x } & = & 10 \color{blue}{-3} \\\Leftrightarrow &7x & = &7\\\Leftrightarrow & \color{red}{7}x & = &7\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{7}{7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{+6}& = & 2 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6-3x } & = & 2 \color{red}{ +3x }\color{blue}{-6-3x } \\\Leftrightarrow & -8x \color{blue}{-3x } & = & 2 \color{blue}{-6} \\\Leftrightarrow &-11x & = &-4\\\Leftrightarrow & \color{red}{-11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+10}& = & -3 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+10}\color{blue}{-10-8x } & = & -3 \color{red}{ +8x }\color{blue}{-10-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -3 \color{blue}{-10} \\\Leftrightarrow &-15x & = &-13\\\Leftrightarrow & \color{red}{-15}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{13}{15} } & & \\ & V = \left\{ \frac{13}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+13}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+13}\color{blue}{-13-5x } & = & 15 \color{red}{ +5x }\color{blue}{-13-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &-14x & = &2\\\Leftrightarrow & \color{red}{-14}x & = &2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-7}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-x } & = & -12 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -12 \color{blue}{+7} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+15}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15-11x } & = & 5 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 5 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-10\\\Leftrightarrow & \color{red}{-5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-10}{-5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+2}& = & 9 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2-5x } & = & 9 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 9 \color{blue}{-2} \\\Leftrightarrow &x & = &7\\\Leftrightarrow & \color{red}{}x & = &7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 7 \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-14}& = & 5 \color{red}{ +14x } \\\Leftrightarrow & 5x \color{red}{-14}\color{blue}{+14-14x } & = & 5 \color{red}{ +14x }\color{blue}{+14-14x } \\\Leftrightarrow & 5x \color{blue}{-14x } & = & 5 \color{blue}{+14} \\\Leftrightarrow &-9x & = &19\\\Leftrightarrow & \color{red}{-9}x & = &19\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{19}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{9} } & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+10}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-x } & = & -15 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -15 \color{blue}{-10} \\\Leftrightarrow &-6x & = &-25\\\Leftrightarrow & \color{red}{-6}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-25}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{25}{6} } & & \\ & V = \left\{ \frac{25}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{+6}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6-5x } & = & 7 \color{red}{ +5x }\color{blue}{-6-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &7x & = &1\\\Leftrightarrow & \color{red}{7}x & = &1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)