Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+12}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12-x } & = & -11 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -11 \color{blue}{-12} \\\Leftrightarrow &-15x & = &-23\\\Leftrightarrow & \color{red}{-15}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-23}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{23}{15} } & & \\ & V = \left\{ \frac{23}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-4}& = & -11 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4+7x } & = & -11 \color{red}{ -7x }\color{blue}{+4+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -11 \color{blue}{+4} \\\Leftrightarrow &22x & = &-7\\\Leftrightarrow & \color{red}{22}x & = &-7\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-7}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{22} } & & \\ & V = \left\{ \frac{-7}{22} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-5}& = & 11 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5-9x } & = & 11 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & 11 \color{blue}{+5} \\\Leftrightarrow &-x & = &16\\\Leftrightarrow & \color{red}{-}x & = &16\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{16}{-1} \\\Leftrightarrow & \color{green}{ x = -16 } & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-3}& = & 4 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{-3}\color{blue}{+3-3x } & = & 4 \color{red}{ +3x }\color{blue}{+3-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & 4 \color{blue}{+3} \\\Leftrightarrow &-17x & = &7\\\Leftrightarrow & \color{red}{-17}x & = &7\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{7}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+6}& = & 9 \color{red}{ +9x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6-9x } & = & 9 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & 5x \color{blue}{-9x } & = & 9 \color{blue}{-6} \\\Leftrightarrow &-4x & = &3\\\Leftrightarrow & \color{red}{-4}x & = &3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-15}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-15}\color{blue}{+15-5x } & = & 15 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 15 \color{blue}{+15} \\\Leftrightarrow &-14x & = &30\\\Leftrightarrow & \color{red}{-14}x & = &30\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{30}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-15}& = & -5 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15-5x } & = & -5 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & 11x \color{blue}{-5x } & = & -5 \color{blue}{+15} \\\Leftrightarrow &6x & = &10\\\Leftrightarrow & \color{red}{6}x & = &10\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{10}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-15}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15-5x } & = & -4 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & -4 \color{blue}{+15} \\\Leftrightarrow &9x & = &11\\\Leftrightarrow & \color{red}{9}x & = &11\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{11}{9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-8}& = & 3 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8+4x } & = & 3 \color{red}{ -4x }\color{blue}{+8+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 3 \color{blue}{+8} \\\Leftrightarrow &13x & = &11\\\Leftrightarrow & \color{red}{13}x & = &11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+2}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-5x } & = & 11 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & 11 \color{blue}{-2} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+6}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6-x } & = & 6 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 6 \color{blue}{-6} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+13}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+13}\color{blue}{-13-x } & = & 11 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 11 \color{blue}{-13} \\\Leftrightarrow &-12x & = &-2\\\Leftrightarrow & \color{red}{-12}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)