Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+5}& = & 9 \color{red}{ +6x } \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5-6x } & = & 9 \color{red}{ +6x }\color{blue}{-5-6x } \\\Leftrightarrow & 13x \color{blue}{-6x } & = & 9 \color{blue}{-5} \\\Leftrightarrow &7x & = &4\\\Leftrightarrow & \color{red}{7}x & = &4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+3}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3-5x } & = & 1 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & 1 \color{blue}{-3} \\\Leftrightarrow &-x & = &-2\\\Leftrightarrow & \color{red}{-}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-2}{-1} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-3}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3-13x } & = & 14 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & 5x \color{blue}{-13x } & = & 14 \color{blue}{+3} \\\Leftrightarrow &-8x & = &17\\\Leftrightarrow & \color{red}{-8}x & = &17\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{17}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{8} } & & \\ & V = \left\{ \frac{-17}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+14}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-7x } & = & -1 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &-20x & = &-15\\\Leftrightarrow & \color{red}{-20}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-15}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-9}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9-x } & = & 13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 13 \color{blue}{+9} \\\Leftrightarrow &9x & = &22\\\Leftrightarrow & \color{red}{9}x & = &22\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{22}{9} \\\Leftrightarrow & \color{green}{ x = \frac{22}{9} } & & \\ & V = \left\{ \frac{22}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-9}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{-9}\color{blue}{+9-13x } & = & -12 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & -12 \color{blue}{+9} \\\Leftrightarrow &-7x & = &-3\\\Leftrightarrow & \color{red}{-7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{-14}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-x } & = & -11 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -11 \color{blue}{+14} \\\Leftrightarrow &-10x & = &3\\\Leftrightarrow & \color{red}{-10}x & = &3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{+4}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4-7x } & = & -14 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &-13x & = &-18\\\Leftrightarrow & \color{red}{-13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-18}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+12}& = & -15 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+12}\color{blue}{-12+8x } & = & -15 \color{red}{ -8x }\color{blue}{-12+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -15 \color{blue}{-12} \\\Leftrightarrow &17x & = &-27\\\Leftrightarrow & \color{red}{17}x & = &-27\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-27}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{17} } & & \\ & V = \left\{ \frac{-27}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{-12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12-x } & = & -8 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -8 \color{blue}{+12} \\\Leftrightarrow &2x & = &4\\\Leftrightarrow & \color{red}{2}x & = &4\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{4}{2} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-2}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-2}\color{blue}{+2-x } & = & -5 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &-12x & = &-3\\\Leftrightarrow & \color{red}{-12}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-8}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-8}\color{blue}{+8-x } & = & -8 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -8 \color{blue}{+8} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)