Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-4}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4-11x } & = & 9 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 9 \color{blue}{+4} \\\Leftrightarrow &-3x & = &13\\\Leftrightarrow & \color{red}{-3}x & = &13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+4}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+4}\color{blue}{-4-x } & = & 8 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 8 \color{blue}{-4} \\\Leftrightarrow &-9x & = &4\\\Leftrightarrow & \color{red}{-9}x & = &4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-14}& = & 8 \color{red}{ +14x } \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14-14x } & = & 8 \color{red}{ +14x }\color{blue}{+14-14x } \\\Leftrightarrow & 3x \color{blue}{-14x } & = & 8 \color{blue}{+14} \\\Leftrightarrow &-11x & = &22\\\Leftrightarrow & \color{red}{-11}x & = &22\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{22}{-11} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+6}& = & 5 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{+6}\color{blue}{-6-4x } & = & 5 \color{red}{ +4x }\color{blue}{-6-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 5 \color{blue}{-6} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-5}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-5}\color{blue}{+5+13x } & = & -5 \color{red}{ -13x }\color{blue}{+5+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -5 \color{blue}{+5} \\\Leftrightarrow &27x & = &0\\\Leftrightarrow & \color{red}{27}x & = &0\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{0}{27} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-4}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-4}\color{blue}{+4-x } & = & 4 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 4 \color{blue}{+4} \\\Leftrightarrow &-10x & = &8\\\Leftrightarrow & \color{red}{-10}x & = &8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+1}& = & -10 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1+2x } & = & -10 \color{red}{ -2x }\color{blue}{-1+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & -10 \color{blue}{-1} \\\Leftrightarrow &7x & = &-11\\\Leftrightarrow & \color{red}{7}x & = &-11\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-11}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-8}& = & -11 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8+3x } & = & -11 \color{red}{ -3x }\color{blue}{+8+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -11 \color{blue}{+8} \\\Leftrightarrow &13x & = &-3\\\Leftrightarrow & \color{red}{13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{+12}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+12}\color{blue}{-12-7x } & = & -9 \color{red}{ +7x }\color{blue}{-12-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -9 \color{blue}{-12} \\\Leftrightarrow &-16x & = &-21\\\Leftrightarrow & \color{red}{-16}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-21}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{21}{16} } & & \\ & V = \left\{ \frac{21}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{-3}& = & -7 \color{red}{ -14x } \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3+14x } & = & -7 \color{red}{ -14x }\color{blue}{+3+14x } \\\Leftrightarrow & x \color{blue}{+14x } & = & -7 \color{blue}{+3} \\\Leftrightarrow &15x & = &-4\\\Leftrightarrow & \color{red}{15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-4}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+13}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+13}\color{blue}{-13-13x } & = & 10 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 10 \color{blue}{-13} \\\Leftrightarrow &-28x & = &-3\\\Leftrightarrow & \color{red}{-28}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-3}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{3}{28} } & & \\ & V = \left\{ \frac{3}{28} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{-12}& = & 15 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{-12}\color{blue}{+12-9x } & = & 15 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & 15 \color{blue}{+12} \\\Leftrightarrow &x & = &27\\\Leftrightarrow & \color{red}{}x & = &27\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 27 \\\Leftrightarrow & \color{green}{ x = 27 } & & \\ & V = \left\{ 27 \right\} & \\\end{align}\)