Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+3}& = & -4 \color{red}{ -8x } \\\Leftrightarrow & -x \color{red}{+3}\color{blue}{-3+8x } & = & -4 \color{red}{ -8x }\color{blue}{-3+8x } \\\Leftrightarrow & -x \color{blue}{+8x } & = & -4 \color{blue}{-3} \\\Leftrightarrow &7x & = &-7\\\Leftrightarrow & \color{red}{7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-7}{7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{-9}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-x } & = & -12 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -12 \color{blue}{+9} \\\Leftrightarrow &-6x & = &-3\\\Leftrightarrow & \color{red}{-6}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-10}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-13x } & = & 13 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &-25x & = &23\\\Leftrightarrow & \color{red}{-25}x & = &23\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{23}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{25} } & & \\ & V = \left\{ \frac{-23}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+14}& = & -10 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14-4x } & = & -10 \color{red}{ +4x }\color{blue}{-14-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & -10 \color{blue}{-14} \\\Leftrightarrow &-x & = &-24\\\Leftrightarrow & \color{red}{-}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-24}{-1} \\\Leftrightarrow & \color{green}{ x = 24 } & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{-9}& = & 5 \color{red}{ -x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9+x } & = & 5 \color{red}{ -x }\color{blue}{+9+x } \\\Leftrightarrow & x \color{blue}{+x } & = & 5 \color{blue}{+9} \\\Leftrightarrow &2x & = &14\\\Leftrightarrow & \color{red}{2}x & = &14\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{14}{2} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-2}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{-2}\color{blue}{+2-13x } & = & 13 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & 13 \color{blue}{+2} \\\Leftrightarrow &-5x & = &15\\\Leftrightarrow & \color{red}{-5}x & = &15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{15}{-5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+5}& = & 2 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-3x } & = & 2 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & 2 \color{blue}{-5} \\\Leftrightarrow &-5x & = &-3\\\Leftrightarrow & \color{red}{-5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+1}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1-x } & = & -9 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -9 \color{blue}{-1} \\\Leftrightarrow &-12x & = &-10\\\Leftrightarrow & \color{red}{-12}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-4}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-4}\color{blue}{+4-x } & = & -15 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -15 \color{blue}{+4} \\\Leftrightarrow &-5x & = &-11\\\Leftrightarrow & \color{red}{-5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+6}& = & 2 \color{red}{ -8x } \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6+8x } & = & 2 \color{red}{ -8x }\color{blue}{-6+8x } \\\Leftrightarrow & -x \color{blue}{+8x } & = & 2 \color{blue}{-6} \\\Leftrightarrow &7x & = &-4\\\Leftrightarrow & \color{red}{7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+8}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8-x } & = & -8 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -8 \color{blue}{-8} \\\Leftrightarrow &-15x & = &-16\\\Leftrightarrow & \color{red}{-15}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-16}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{16}{15} } & & \\ & V = \left\{ \frac{16}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+12}& = & 8 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+12}\color{blue}{-12+15x } & = & 8 \color{red}{ -15x }\color{blue}{-12+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 8 \color{blue}{-12} \\\Leftrightarrow &19x & = &-4\\\Leftrightarrow & \color{red}{19}x & = &-4\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-4}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)