Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+7}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7-x } & = & 11 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 11 \color{blue}{-7} \\\Leftrightarrow &-9x & = &4\\\Leftrightarrow & \color{red}{-9}x & = &4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+9}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9-7x } & = & -3 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & -3 \color{blue}{-9} \\\Leftrightarrow &-x & = &-12\\\Leftrightarrow & \color{red}{-}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-12}{-1} \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+10}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-x } & = & -11 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -11 \color{blue}{-10} \\\Leftrightarrow &-6x & = &-21\\\Leftrightarrow & \color{red}{-6}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-21}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+6}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+6}\color{blue}{-6+11x } & = & 2 \color{red}{ -11x }\color{blue}{-6+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & 2 \color{blue}{-6} \\\Leftrightarrow &25x & = &-4\\\Leftrightarrow & \color{red}{25}x & = &-4\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-4}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{25} } & & \\ & V = \left\{ \frac{-4}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+12}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+12}\color{blue}{-12-x } & = & 4 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 4 \color{blue}{-12} \\\Leftrightarrow &-4x & = &-8\\\Leftrightarrow & \color{red}{-4}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-8}{-4} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-13}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-11x } & = & 3 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 3 \color{blue}{+13} \\\Leftrightarrow &-9x & = &16\\\Leftrightarrow & \color{red}{-9}x & = &16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{9} } & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+15}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15-x } & = & -14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -14 \color{blue}{-15} \\\Leftrightarrow &7x & = &-29\\\Leftrightarrow & \color{red}{7}x & = &-29\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-29}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{7} } & & \\ & V = \left\{ \frac{-29}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+3}& = & -12 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3+14x } & = & -12 \color{red}{ -14x }\color{blue}{-3+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -12 \color{blue}{-3} \\\Leftrightarrow &19x & = &-15\\\Leftrightarrow & \color{red}{19}x & = &-15\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-15}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{19} } & & \\ & V = \left\{ \frac{-15}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-5}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-x } & = & -15 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -15 \color{blue}{+5} \\\Leftrightarrow &-9x & = &-10\\\Leftrightarrow & \color{red}{-9}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{10}{9} } & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{-12}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12-x } & = & 7 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 7 \color{blue}{+12} \\\Leftrightarrow &-10x & = &19\\\Leftrightarrow & \color{red}{-10}x & = &19\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{19}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{10} } & & \\ & V = \left\{ \frac{-19}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-7}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-7}\color{blue}{+7-x } & = & 4 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 4 \color{blue}{+7} \\\Leftrightarrow &5x & = &11\\\Leftrightarrow & \color{red}{5}x & = &11\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{11}{5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-4}\color{blue}{+4-x } & = & 5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &-4x & = &9\\\Leftrightarrow & \color{red}{-4}x & = &9\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{9}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)