Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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