Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-4}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-4}\color{blue}{+4-7x } & = & -12 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & -12 \color{blue}{+4} \\\Leftrightarrow &2x & = &-8\\\Leftrightarrow & \color{red}{2}x & = &-8\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-8}{2} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-10}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-x } & = & 3 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 3 \color{blue}{+10} \\\Leftrightarrow &-13x & = &13\\\Leftrightarrow & \color{red}{-13}x & = &13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{13}{-13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+9}& = & -9 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{+9}\color{blue}{-9-9x } & = & -9 \color{red}{ +9x }\color{blue}{-9-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &-11x & = &-18\\\Leftrightarrow & \color{red}{-11}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+14}& = & -3 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+14}\color{blue}{-14+7x } & = & -3 \color{red}{ -7x }\color{blue}{-14+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &15x & = &-17\\\Leftrightarrow & \color{red}{15}x & = &-17\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-17}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{15} } & & \\ & V = \left\{ \frac{-17}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+5}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5-x } & = & 9 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 9 \color{blue}{-5} \\\Leftrightarrow &9x & = &4\\\Leftrightarrow & \color{red}{9}x & = &4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-6}& = & -2 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6-4x } & = & -2 \color{red}{ +4x }\color{blue}{+6-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & -2 \color{blue}{+6} \\\Leftrightarrow &5x & = &4\\\Leftrightarrow & \color{red}{5}x & = &4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+5}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{+5}\color{blue}{-5-13x } & = & 11 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & 11 \color{blue}{-5} \\\Leftrightarrow &-4x & = &6\\\Leftrightarrow & \color{red}{-4}x & = &6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2-x } & = & 15 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & 15 \color{blue}{+2} \\\Leftrightarrow &8x & = &17\\\Leftrightarrow & \color{red}{8}x & = &17\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{17}{8} \\\Leftrightarrow & \color{green}{ x = \frac{17}{8} } & & \\ & V = \left\{ \frac{17}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-12}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-12}\color{blue}{+12-9x } & = & -13 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & -13 \color{blue}{+12} \\\Leftrightarrow &-20x & = &-1\\\Leftrightarrow & \color{red}{-20}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-1}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{20} } & & \\ & V = \left\{ \frac{1}{20} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-13}& = & 12 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13-10x } & = & 12 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 12 \color{blue}{+13} \\\Leftrightarrow &-13x & = &25\\\Leftrightarrow & \color{red}{-13}x & = &25\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{25}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{13} } & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-9}& = & 14 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9+11x } & = & 14 \color{red}{ -11x }\color{blue}{+9+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 14 \color{blue}{+9} \\\Leftrightarrow &26x & = &23\\\Leftrightarrow & \color{red}{26}x & = &23\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{23}{26} \\\Leftrightarrow & \color{green}{ x = \frac{23}{26} } & & \\ & V = \left\{ \frac{23}{26} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+3}& = & 12 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{+3}\color{blue}{-3-5x } & = & 12 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & 12 \color{blue}{-3} \\\Leftrightarrow &-7x & = &9\\\Leftrightarrow & \color{red}{-7}x & = &9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)