Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+13}& = & -1 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13+5x } & = & -1 \color{red}{ -5x }\color{blue}{-13+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -1 \color{blue}{-13} \\\Leftrightarrow &16x & = &-14\\\Leftrightarrow & \color{red}{16}x & = &-14\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-14}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-2}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-2}\color{blue}{+2-x } & = & 7 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 7 \color{blue}{+2} \\\Leftrightarrow &-9x & = &9\\\Leftrightarrow & \color{red}{-9}x & = &9\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{9}{-9} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+8}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+8}\color{blue}{-8-x } & = & 8 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 8 \color{blue}{-8} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-8}& = & 7 \color{red}{ -13x } \\\Leftrightarrow & x \color{red}{-8}\color{blue}{+8+13x } & = & 7 \color{red}{ -13x }\color{blue}{+8+13x } \\\Leftrightarrow & x \color{blue}{+13x } & = & 7 \color{blue}{+8} \\\Leftrightarrow &14x & = &15\\\Leftrightarrow & \color{red}{14}x & = &15\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{15}{14} \\\Leftrightarrow & \color{green}{ x = \frac{15}{14} } & & \\ & V = \left\{ \frac{15}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-10}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-10}\color{blue}{+10-x } & = & 10 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & 10 \color{blue}{+10} \\\Leftrightarrow &8x & = &20\\\Leftrightarrow & \color{red}{8}x & = &20\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{20}{8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{-12}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12-13x } & = & -9 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & -9 \color{blue}{+12} \\\Leftrightarrow &-10x & = &3\\\Leftrightarrow & \color{red}{-10}x & = &3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+11}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+11}\color{blue}{-11-x } & = & -1 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &-5x & = &-12\\\Leftrightarrow & \color{red}{-5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{-1}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-1}\color{blue}{+1+11x } & = & 7 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 7 \color{blue}{+1} \\\Leftrightarrow &26x & = &8\\\Leftrightarrow & \color{red}{26}x & = &8\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{8}{26} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{+3}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3-x } & = & 14 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 14 \color{blue}{-3} \\\Leftrightarrow &-6x & = &11\\\Leftrightarrow & \color{red}{-6}x & = &11\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{11}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+15}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15-x } & = & -5 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -5 \color{blue}{-15} \\\Leftrightarrow &12x & = &-20\\\Leftrightarrow & \color{red}{12}x & = &-20\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-20}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{+8}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8-11x } & = & 3 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & 7x \color{blue}{-11x } & = & 3 \color{blue}{-8} \\\Leftrightarrow &-4x & = &-5\\\Leftrightarrow & \color{red}{-4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+15}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15-x } & = & 2 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 2 \color{blue}{-15} \\\Leftrightarrow &-6x & = &-13\\\Leftrightarrow & \color{red}{-6}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)