Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+3}& = & 10 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3-8x } & = & 10 \color{red}{ +8x }\color{blue}{-3-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 10 \color{blue}{-3} \\\Leftrightarrow &-15x & = &7\\\Leftrightarrow & \color{red}{-15}x & = &7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{+8}& = & -11 \color{red}{ -3x } \\\Leftrightarrow & 13x \color{red}{+8}\color{blue}{-8+3x } & = & -11 \color{red}{ -3x }\color{blue}{-8+3x } \\\Leftrightarrow & 13x \color{blue}{+3x } & = & -11 \color{blue}{-8} \\\Leftrightarrow &16x & = &-19\\\Leftrightarrow & \color{red}{16}x & = &-19\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-19}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{16} } & & \\ & V = \left\{ \frac{-19}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5-x } & = & 13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &5x & = &18\\\Leftrightarrow & \color{red}{5}x & = &18\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{18}{5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-11}& = & -8 \color{red}{ +12x } \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11-12x } & = & -8 \color{red}{ +12x }\color{blue}{+11-12x } \\\Leftrightarrow & 7x \color{blue}{-12x } & = & -8 \color{blue}{+11} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+7}& = & 5 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+7}\color{blue}{-7-10x } & = & 5 \color{red}{ +10x }\color{blue}{-7-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 5 \color{blue}{-7} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+5}& = & -12 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{+5}\color{blue}{-5+7x } & = & -12 \color{red}{ -7x }\color{blue}{-5+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & -12 \color{blue}{-5} \\\Leftrightarrow &12x & = &-17\\\Leftrightarrow & \color{red}{12}x & = &-17\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-17}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{12} } & & \\ & V = \left\{ \frac{-17}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+7}& = & -11 \color{red}{ -5x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7+5x } & = & -11 \color{red}{ -5x }\color{blue}{-7+5x } \\\Leftrightarrow & x \color{blue}{+5x } & = & -11 \color{blue}{-7} \\\Leftrightarrow &6x & = &-18\\\Leftrightarrow & \color{red}{6}x & = &-18\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-18}{6} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-3}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3+11x } & = & 3 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 3 \color{blue}{+3} \\\Leftrightarrow &17x & = &6\\\Leftrightarrow & \color{red}{17}x & = &6\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{6}{17} \\\Leftrightarrow & \color{green}{ x = \frac{6}{17} } & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-10}& = & -7 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{-10}\color{blue}{+10-14x } & = & -7 \color{red}{ +14x }\color{blue}{+10-14x } \\\Leftrightarrow & 15x \color{blue}{-14x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &x & = &3\\\Leftrightarrow & \color{red}{}x & = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-11}& = & -6 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11+8x } & = & -6 \color{red}{ -8x }\color{blue}{+11+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -6 \color{blue}{+11} \\\Leftrightarrow &17x & = &5\\\Leftrightarrow & \color{red}{17}x & = &5\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{5}{17} \\\Leftrightarrow & \color{green}{ x = \frac{5}{17} } & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-2}\color{blue}{+2-x } & = & -10 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -10 \color{blue}{+2} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-5}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-x } & = & 8 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 8 \color{blue}{+5} \\\Leftrightarrow &-9x & = &13\\\Leftrightarrow & \color{red}{-9}x & = &13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)