Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{-15}& = & 3 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15-8x } & = & 3 \color{red}{ +8x }\color{blue}{+15-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & 3 \color{blue}{+15} \\\Leftrightarrow &-x & = &18\\\Leftrightarrow & \color{red}{-}x & = &18\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{18}{-1} \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+10}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+10}\color{blue}{-10-11x } & = & -1 \color{red}{ +11x }\color{blue}{-10-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -1 \color{blue}{-10} \\\Leftrightarrow &x & = &-11\\\Leftrightarrow & \color{red}{}x & = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-9}& = & -4 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9+11x } & = & -4 \color{red}{ -11x }\color{blue}{+9+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -4 \color{blue}{+9} \\\Leftrightarrow &23x & = &5\\\Leftrightarrow & \color{red}{23}x & = &5\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{5}{23} \\\Leftrightarrow & \color{green}{ x = \frac{5}{23} } & & \\ & V = \left\{ \frac{5}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-7}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7-x } & = & 12 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 12 \color{blue}{+7} \\\Leftrightarrow &-16x & = &19\\\Leftrightarrow & \color{red}{-16}x & = &19\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{19}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{16} } & & \\ & V = \left\{ \frac{-19}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+3}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{+3}\color{blue}{-3-13x } & = & 3 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & 3 \color{blue}{-3} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-3}& = & -9 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3+3x } & = & -9 \color{red}{ -3x }\color{blue}{+3+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -9 \color{blue}{+3} \\\Leftrightarrow &10x & = &-6\\\Leftrightarrow & \color{red}{10}x & = &-6\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-6}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+3}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+3}\color{blue}{-3-x } & = & 12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 12 \color{blue}{-3} \\\Leftrightarrow &13x & = &9\\\Leftrightarrow & \color{red}{13}x & = &9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-3}& = & -4 \color{red}{ +2x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3-2x } & = & -4 \color{red}{ +2x }\color{blue}{+3-2x } \\\Leftrightarrow & 13x \color{blue}{-2x } & = & -4 \color{blue}{+3} \\\Leftrightarrow &11x & = &-1\\\Leftrightarrow & \color{red}{11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-14}& = & -5 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14-10x } & = & -5 \color{red}{ +10x }\color{blue}{+14-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & -5 \color{blue}{+14} \\\Leftrightarrow &-x & = &9\\\Leftrightarrow & \color{red}{-}x & = &9\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{9}{-1} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-x } & = & 4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &-8x & = &-10\\\Leftrightarrow & \color{red}{-8}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-10}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+11}& = & 9 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11+2x } & = & 9 \color{red}{ -2x }\color{blue}{-11+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & 9 \color{blue}{-11} \\\Leftrightarrow &5x & = &-2\\\Leftrightarrow & \color{red}{5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-4}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4-7x } & = & 4 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & 5x \color{blue}{-7x } & = & 4 \color{blue}{+4} \\\Leftrightarrow &-2x & = &8\\\Leftrightarrow & \color{red}{-2}x & = &8\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{8}{-2} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)