Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{+2}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+2}\color{blue}{-2-x } & = & -11 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -11 \color{blue}{-2} \\\Leftrightarrow &-3x & = &-13\\\Leftrightarrow & \color{red}{-3}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-4}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4-x } & = & -10 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -10 \color{blue}{+4} \\\Leftrightarrow &5x & = &-6\\\Leftrightarrow & \color{red}{5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+8}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+8}\color{blue}{-8-x } & = & -15 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -15 \color{blue}{-8} \\\Leftrightarrow &-10x & = &-23\\\Leftrightarrow & \color{red}{-10}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-23}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{23}{10} } & & \\ & V = \left\{ \frac{23}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+12}& = & 3 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12+2x } & = & 3 \color{red}{ -2x }\color{blue}{-12+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & 3 \color{blue}{-12} \\\Leftrightarrow &5x & = &-9\\\Leftrightarrow & \color{red}{5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-5}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5-x } & = & 12 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &-16x & = &17\\\Leftrightarrow & \color{red}{-16}x & = &17\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{17}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{16} } & & \\ & V = \left\{ \frac{-17}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-3}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3-x } & = & 10 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &-12x & = &13\\\Leftrightarrow & \color{red}{-12}x & = &13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{12} } & & \\ & V = \left\{ \frac{-13}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+6}& = & 15 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6-9x } & = & 15 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 15 \color{blue}{-6} \\\Leftrightarrow &-13x & = &9\\\Leftrightarrow & \color{red}{-13}x & = &9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-5}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-5x } & = & -8 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -8 \color{blue}{+5} \\\Leftrightarrow &-9x & = &-3\\\Leftrightarrow & \color{red}{-9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+11}& = & -10 \color{red}{ +10x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-10x } & = & -10 \color{red}{ +10x }\color{blue}{-11-10x } \\\Leftrightarrow & -13x \color{blue}{-10x } & = & -10 \color{blue}{-11} \\\Leftrightarrow &-23x & = &-21\\\Leftrightarrow & \color{red}{-23}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-21}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{21}{23} } & & \\ & V = \left\{ \frac{21}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+13}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{+13}\color{blue}{-13-9x } & = & -10 \color{red}{ +9x }\color{blue}{-13-9x } \\\Leftrightarrow & 7x \color{blue}{-9x } & = & -10 \color{blue}{-13} \\\Leftrightarrow &-2x & = &-23\\\Leftrightarrow & \color{red}{-2}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-23}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{23}{2} } & & \\ & V = \left\{ \frac{23}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+7}& = & 6 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7-14x } & = & 6 \color{red}{ +14x }\color{blue}{-7-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & 6 \color{blue}{-7} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-7}& = & -3 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-7}\color{blue}{+7+8x } & = & -3 \color{red}{ -8x }\color{blue}{+7+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -3 \color{blue}{+7} \\\Leftrightarrow &17x & = &4\\\Leftrightarrow & \color{red}{17}x & = &4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)