Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{-2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-2}\color{blue}{+2-x } & = & -10 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -10 \color{blue}{+2} \\\Leftrightarrow &-5x & = &-8\\\Leftrightarrow & \color{red}{-5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+7}& = & 5 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{+7}\color{blue}{-7+8x } & = & 5 \color{red}{ -8x }\color{blue}{-7+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 5 \color{blue}{-7} \\\Leftrightarrow &19x & = &-2\\\Leftrightarrow & \color{red}{19}x & = &-2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{19} } & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-8}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8-x } & = & 5 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 5 \color{blue}{+8} \\\Leftrightarrow &-16x & = &13\\\Leftrightarrow & \color{red}{-16}x & = &13\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{13}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{16} } & & \\ & V = \left\{ \frac{-13}{16} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-9}& = & 6 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9+8x } & = & 6 \color{red}{ -8x }\color{blue}{+9+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &17x & = &15\\\Leftrightarrow & \color{red}{17}x & = &15\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{15}{17} \\\Leftrightarrow & \color{green}{ x = \frac{15}{17} } & & \\ & V = \left\{ \frac{15}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{-7}& = & -15 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7+12x } & = & -15 \color{red}{ -12x }\color{blue}{+7+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & -15 \color{blue}{+7} \\\Leftrightarrow &17x & = &-8\\\Leftrightarrow & \color{red}{17}x & = &-8\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-8}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{17} } & & \\ & V = \left\{ \frac{-8}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+3}& = & 2 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3-4x } & = & 2 \color{red}{ +4x }\color{blue}{-3-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & 2 \color{blue}{-3} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{-11}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11-x } & = & -6 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -6 \color{blue}{+11} \\\Leftrightarrow &-16x & = &5\\\Leftrightarrow & \color{red}{-16}x & = &5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{16} } & & \\ & V = \left\{ \frac{-5}{16} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+15}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{+15}\color{blue}{-15-13x } & = & 8 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & 8 \color{blue}{-15} \\\Leftrightarrow &-15x & = &-7\\\Leftrightarrow & \color{red}{-15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+12}& = & -1 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12-14x } & = & -1 \color{red}{ +14x }\color{blue}{-12-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & -1 \color{blue}{-12} \\\Leftrightarrow &-3x & = &-13\\\Leftrightarrow & \color{red}{-3}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{+12}& = & 9 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+12}\color{blue}{-12-10x } & = & 9 \color{red}{ +10x }\color{blue}{-12-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &-13x & = &-3\\\Leftrightarrow & \color{red}{-13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{+12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+12}\color{blue}{-12-x } & = & -8 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &13x & = &-20\\\Leftrightarrow & \color{red}{13}x & = &-20\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-20}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{13} } & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-13}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{-13}\color{blue}{+13-11x } & = & 14 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 14 \color{blue}{+13} \\\Leftrightarrow &-3x & = &27\\\Leftrightarrow & \color{red}{-3}x & = &27\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{27}{-3} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)