Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+12}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-5x } & = & -7 \color{red}{ +5x }\color{blue}{-12-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -7 \color{blue}{-12} \\\Leftrightarrow &-9x & = &-19\\\Leftrightarrow & \color{red}{-9}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-19}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{19}{9} } & & \\ & V = \left\{ \frac{19}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+9}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+9}\color{blue}{-9-x } & = & 1 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 1 \color{blue}{-9} \\\Leftrightarrow &7x & = &-8\\\Leftrightarrow & \color{red}{7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-8}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+4}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-x } & = & 13 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 13 \color{blue}{-4} \\\Leftrightarrow &-10x & = &9\\\Leftrightarrow & \color{red}{-10}x & = &9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+5}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5-13x } & = & 5 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & 5 \color{blue}{-5} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-13}& = & 1 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13-3x } & = & 1 \color{red}{ +3x }\color{blue}{+13-3x } \\\Leftrightarrow & -8x \color{blue}{-3x } & = & 1 \color{blue}{+13} \\\Leftrightarrow &-11x & = &14\\\Leftrightarrow & \color{red}{-11}x & = &14\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{14}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+2}& = & -2 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2+13x } & = & -2 \color{red}{ -13x }\color{blue}{-2+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -2 \color{blue}{-2} \\\Leftrightarrow &24x & = &-4\\\Leftrightarrow & \color{red}{24}x & = &-4\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-4}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-1}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-9x } & = & 8 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 8 \color{blue}{+1} \\\Leftrightarrow &-17x & = &9\\\Leftrightarrow & \color{red}{-17}x & = &9\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{9}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{17} } & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+14}& = & -15 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+14}\color{blue}{-14+13x } & = & -15 \color{red}{ -13x }\color{blue}{-14+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -15 \color{blue}{-14} \\\Leftrightarrow &22x & = &-29\\\Leftrightarrow & \color{red}{22}x & = &-29\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-29}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{22} } & & \\ & V = \left\{ \frac{-29}{22} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-1}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & -6 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -6 \color{blue}{+1} \\\Leftrightarrow &-15x & = &-5\\\Leftrightarrow & \color{red}{-15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-4}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-4}\color{blue}{+4-x } & = & 9 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 9 \color{blue}{+4} \\\Leftrightarrow &-6x & = &13\\\Leftrightarrow & \color{red}{-6}x & = &13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-1}& = & 7 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1-3x } & = & 7 \color{red}{ +3x }\color{blue}{+1-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 7 \color{blue}{+1} \\\Leftrightarrow &-8x & = &8\\\Leftrightarrow & \color{red}{-8}x & = &8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{8}{-8} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-4}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-4}\color{blue}{+4-x } & = & 1 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 1 \color{blue}{+4} \\\Leftrightarrow &-14x & = &5\\\Leftrightarrow & \color{red}{-14}x & = &5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{14} } & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)