Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-11}& = & 6 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-11}\color{blue}{+11+12x } & = & 6 \color{red}{ -12x }\color{blue}{+11+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & 6 \color{blue}{+11} \\\Leftrightarrow &25x & = &17\\\Leftrightarrow & \color{red}{25}x & = &17\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{17}{25} \\\Leftrightarrow & \color{green}{ x = \frac{17}{25} } & & \\ & V = \left\{ \frac{17}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+5}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5-5x } & = & -2 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & -2 \color{blue}{-5} \\\Leftrightarrow &-x & = &-7\\\Leftrightarrow & \color{red}{-}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-7}{-1} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-11}& = & 15 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-11}\color{blue}{+11+14x } & = & 15 \color{red}{ -14x }\color{blue}{+11+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & 15 \color{blue}{+11} \\\Leftrightarrow &19x & = &26\\\Leftrightarrow & \color{red}{19}x & = &26\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{26}{19} \\\Leftrightarrow & \color{green}{ x = \frac{26}{19} } & & \\ & V = \left\{ \frac{26}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+11}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+11}\color{blue}{-11-x } & = & -7 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -7 \color{blue}{-11} \\\Leftrightarrow &-12x & = &-18\\\Leftrightarrow & \color{red}{-12}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-18}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+13}& = & 15 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+13}\color{blue}{-13+3x } & = & 15 \color{red}{ -3x }\color{blue}{-13+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &7x & = &2\\\Leftrightarrow & \color{red}{7}x & = &2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+15}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+15}\color{blue}{-15-x } & = & -5 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -5 \color{blue}{-15} \\\Leftrightarrow &-16x & = &-20\\\Leftrightarrow & \color{red}{-16}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-20}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-4}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-4}\color{blue}{+4-13x } & = & 9 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 9 \color{blue}{+4} \\\Leftrightarrow &-19x & = &13\\\Leftrightarrow & \color{red}{-19}x & = &13\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{13}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{19} } & & \\ & V = \left\{ \frac{-13}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+9}& = & 11 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+9}\color{blue}{-9+3x } & = & 11 \color{red}{ -3x }\color{blue}{-9+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 11 \color{blue}{-9} \\\Leftrightarrow &13x & = &2\\\Leftrightarrow & \color{red}{13}x & = &2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+2}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2-7x } & = & 9 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & 9 \color{blue}{-2} \\\Leftrightarrow &-x & = &7\\\Leftrightarrow & \color{red}{-}x & = &7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{7}{-1} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-6}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-6}\color{blue}{+6-x } & = & -9 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -9 \color{blue}{+6} \\\Leftrightarrow &-9x & = &-3\\\Leftrightarrow & \color{red}{-9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-9}& = & -5 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-3x } & = & -5 \color{red}{ +3x }\color{blue}{+9-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -5 \color{blue}{+9} \\\Leftrightarrow &-5x & = &4\\\Leftrightarrow & \color{red}{-5}x & = &4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{+2}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+2}\color{blue}{-2-7x } & = & -7 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & -7 \color{blue}{-2} \\\Leftrightarrow &-4x & = &-9\\\Leftrightarrow & \color{red}{-4}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-9}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)